Chapter 4.2, Problem 12SE

a.

a.

To determine

Find the median, midrange and geometric mean of the vehicle speeds on the highway I-5.

Answer to Problem 12SE

The median of the vehicle speed is 68.

The geometric mean of the vehicle speed is 67.37013.

The midrange of the vehicle speed is 68.

Explanation of Solution

The speeds of 9 vehicles on highway I-5 are 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:

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:

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:

• Thus, the midrange is 68.

b.

To determine

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

Answer to Problem 12SE

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

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Median and mid-range have equal values. Although the geometric mean is slightly different, the value is still quite close to the values of median and mid-range. In this context, all the measures like median, midrange and geometric mean have nearer values. So, it is assumed to be acceptable.

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

b.

a.

To determine

Find the median, midrange and geometric mean of the sodium grams in the canned soup.

Answer to Problem 12SE

The median of the sodium grams is 303.

The geometric mean of the sodium grams is 300.9403.

The midrange of the sodium grams is 295.5.

Explanation of Solution

The sodium grams in 8 varieties of canned soup are 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:

Thus, the median is 303.

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:

Thus, the geometric mean is 300.9403.

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:

• Thus, the midrange is 295.5.

b.

To determine

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

Answer to Problem 12SE

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

Explanation of Solution

From the data, it is observed that there occurs no extreme value. Although the values of median, midrange and geometric mean are not equal, they are still quite close to each other. So, it is assumed to be acceptable.

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

c.

a.

To determine

Find the median, midrange and geometric mean of the annual campus health visits of 12 students.

Answer to Problem 12SE

The median of the annual campus health visit is 1.5.

The Geometric mean of the annual campus health visit is not applicable.

The midrange of the annual campus health visit is 7.5.

Explanation of Solution

The annual campus health center visits of 12 students are 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:

Thus, the median is 1.5.

Geometric mean:

Here, the observations contain the value zero. As a result, the product of the values becomes zero and 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:

• Thus, the midrange is 7.5.

b.

To determine

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

Answer to Problem 12SE

No, the given measures are not all reasonable measures of central 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. Moreover, the value of the geometric mean is not defined. So, the measures are not all acceptable.

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