APPLIED STAT.IN BUS.+ECONOMICS
APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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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.

a.

a.

Expert Solution
Check Mark

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 nth 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:

APPLIED STAT.IN BUS.+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:

APPLIED STAT.IN BUS.+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:

APPLIED STAT.IN BUS.+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 central tendency.

b.

Expert Solution
Check Mark

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.

b.

a.

Expert Solution
Check Mark

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:

APPLIED STAT.IN BUS.+ECONOMICS, Chapter 4.2, Problem 12SE , additional homework tip 4

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:

APPLIED STAT.IN BUS.+ECONOMICS, Chapter 4.2, Problem 12SE , additional homework tip 5

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:

APPLIED STAT.IN BUS.+ECONOMICS, Chapter 4.2, Problem 12SE , additional homework tip 6

  • Thus, the midrange is 295.5.

b.

To determine

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

b.

Expert Solution
Check Mark

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.

c.

a.

Expert Solution
Check Mark

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:

APPLIED STAT.IN BUS.+ECONOMICS, Chapter 4.2, Problem 12SE , additional homework tip 7

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:

APPLIED STAT.IN BUS.+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 central tendency.

b.

Expert Solution
Check Mark

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.

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Chapter 4 Solutions

APPLIED STAT.IN BUS.+ECONOMICS

Ch. 4.2 - (a) For each data set, find the mean, median, and...Ch. 4.2 - For each data set, is the mode a good measure of...Ch. 4.2 - For each data set, is the mode a good measure of...Ch. 4.2 - For each data set, which best indicates a typical...Ch. 4.2 - For each data set, which best indicates a typical...Ch. 4.2 - Days on the market are shown for the 36 most...Ch. 4.2 - Scores are shown for the most recent state civil...Ch. 4.2 - A vehicle emissions testing facility can process...Ch. 4.2 - CitiBank recorded the number of customers to use a...Ch. 4.2 - Prob. 10SE
Ch. 4.2 - Prob. 11SECh. 4.2 - Prob. 12SECh. 4.2 - (a) Write the Excel function for the 10 percent...Ch. 4.2 - Prob. 14SECh. 4.2 - Prob. 15SECh. 4.2 - Spirit Airlines kept track of the number of empty...Ch. 4.2 - CitiBank recorded the number of customers to use a...Ch. 4.2 - On Friday night, the owner of Chez Pierre in...Ch. 4.2 - Prob. 19SECh. 4.2 - The number of internet users in Latin America grew...Ch. 4.3 - (a) Find the mean and standard deviation for each...Ch. 4.3 - For each data set: (a) Find the mean. (b) Find the...Ch. 4.3 - In fuel economy tests in city driving conditions,...Ch. 4.3 - Over the past month, Bobs bowling score mean was...Ch. 4.3 - Prob. 25SECh. 4.3 - Prob. 26SECh. 4.3 - (a) Find the coefficient of variation for prices...Ch. 4.3 - Prob. 28SECh. 4.3 - Noodles and Company tested consumer reaction to...Ch. 4.4 - (a) By Chebyshevs Theorem, at least how many...Ch. 4.4 - An exam has a mean of 70 with a standard deviation...Ch. 4.4 - Prob. 32SECh. 4.4 - The mean collection period for accounts receivable...Ch. 4.4 - Convert each individual data value to a...Ch. 4.4 - Prob. 35SECh. 4.4 - Prob. 36SECh. 4.4 - Find the original data value corresponding to each...Ch. 4.4 - CitiBank recorded the number of customers to use a...Ch. 4.4 - Prob. 39SECh. 4.5 - Scores on an accounting exam ranged from 42 to 96,...Ch. 4.5 - In 2007, total compensation (in thousands of...Ch. 4.5 - Waiting times (minutes) for a table at Joeys BBQ...Ch. 4.5 - Coffee temperatures (degrees Fahrenheit) at a...Ch. 4.5 - Prob. 44SECh. 4.5 - On San Martin Boulevard, embedded sensors kept...Ch. 4.5 - Prob. 46SECh. 4.5 - Prob. 47SECh. 4.6 - For each X-Y data set (n = 12): (a) Make a scatter...Ch. 4.6 - Closing prices of two stocks are recorded for 50...Ch. 4.6 - Prob. 50SECh. 4.6 - Prob. 51SECh. 4.7 - Estimate the mean from this table of grouped data...Ch. 4.7 - Estimate the mean from the following table of...Ch. 4 - What are descriptive statistics? How do they...Ch. 4 - Explain each concept: (a) center, (b) variability,...Ch. 4 - Prob. 3CRCh. 4 - List strengths and weaknesses of each measure of...Ch. 4 - Prob. 5CRCh. 4 - (a) What is a bimodal distribution? (b) Explain...Ch. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - (a) Which standard deviation formula (population,...Ch. 4 - (a) To what kind of data does Chebyshevs Theorem...Ch. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - (a) Explain the method of medians for calculating...Ch. 4 - (a) What is a box plot? What does it tell us? (b)...Ch. 4 - Prob. 17CRCh. 4 - Prob. 18CRCh. 4 - Prob. 19CRCh. 4 - (a) What is kurtosis? 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