Find the median , midrange and geometric mean of the Exam scores of 9 students.

Question

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.

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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.

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Answer 5

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.

Answer 6

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

Answer 7

Chapter 4.2, Problem 12SE

a.

To determine

Find the median, midrange and geometric mean of the Exam scores of 9 students.

Answer 8

a.

Expert Solution

Answer to Problem 12SE

The median of the Exam scores of 9 students is 68.

The geometric mean of the Exam scores of 9 students is 67.37013.

The midrange of the Exam scores of 9 students is 68.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The Exam scores of 9 students is given.

Measures of center:

Median is the middle value in an ordered sequence of data.
Geometric mean is the multiplication all the data values in the sample by taking n^th root of the product and will be affected in the case of zeros and negative values in the observation.
Midrange is the point between the lowest and highest values of X that occurs in halfway.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=MEDIAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 1

Thus, the median is 68.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=GEOMEAN(J1:J9)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 2

Thus, the geometric mean is 67.37013.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column J in cells J1 to J9.
In cell A1, enter the formula “=(MIN(J1:J9)”+MAX(J1:J9))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 3

Thus, the midrange is 68.

Answer 13

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

Answer 14

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

Answer 15

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

From the data, it is observed that there occurs one extreme value. Median and mid-range has similar values. However, mid-range is influenced by the extreme values. In this context, all the measures like median, midrange and geometric mean have the nearer values. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

Answer 20

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

Answer 21

A (b).

To determine

Find the median, midrange and geometric mean of the GPAs of 8 students.

Answer 22

A (b).

Expert Solution

Answer to Problem 12SE

The median of the GPAs of 8 students is 3.03.

The geometric mean of the GPAs of 8 students is 3.009403.

The midrange of the GPAs of 8 students is 2.955.

Answer 23

A (b).

Expert Solution

Answer 24

A (b).

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The GPAs of 8 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=MEDIAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 4

Thus, the median is 3.03.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=GEOMEAN(K1:K8)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 5

Thus, the geometric mean is 3.009403.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column K in cells K1 to K8.
In cell A1, enter the formula “=(MIN(K1:K8)+MAX(K1:K8))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 6

Thus, the midrange is 2.955.

Answer 27

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

Answer 28

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

Answer 29

b.

Expert Solution

Answer to Problem 12SE

Yes, the given measures are reasonable measures of center tendency.

Answer 30

b.

Expert Solution

Answer 31

b.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range has similar values. In this context, all the measures like median, midrange and geometric mean have values nearer to each other. So, it is assumed to be acceptable.

Hence, the given measures are reasonable measures of center tendency.

Answer 34

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

Answer 35

a.

To determine

Find the median, midrange and geometric mean of the class absences of 12 students.

Answer 36

a.

Expert Solution

Answer to Problem 12SE

The median of the class absences of 12 students is 1.5.

The Geometric mean of the class absences of 12 students is not applicable.

The midrange of the class absences of 12 students is 7.5.

Answer 37

a.

Expert Solution

Answer 38

a.

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

The class absence of 12 students is given.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=MEDIAN(L1:L12)”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 7

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain zero. As a result, the geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

Open an EXCEL file.
Enter the data in the column L in cells L1 to L12.
In cell A1, enter the formula “=(MIN(L1:L12)+MAX(L1:L12))/2”.
Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 12SE , additional homework tip 8

Thus, the midrange is 7.5.

Answer 41

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.

Answer 42

b.

To determine

Decide whether the given measures are reasonable measures of center tendency.

Answer 43

b.

Expert Solution

Answer to Problem 12SE

No, the given measures are not all reasonable measures of center tendency

Answer 44

b.

Expert Solution

Answer 45

b.

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

From the data, it is observed that there occurs one extreme value, 15. Median and mid-range have extremely different values. The value of the geometric mean is not defined. So, the measures are not acceptable.

Hence, the given measures are not reasonable measures of center tendency.