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Chapter 2: Q67E (page 104)

Question: Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability

behaviors of CPA corporations, Exercise 2.48 (p. 96). Numerical measures of variation for level of support for the 992 senior managers are shown in the accompanying Minitab printout.

Descriptive Statistics: Support

Variable

N

Mean

StDev.

Variance

Minimum

Maximum

Range

Support

992

67.755

26.871

722.036

0.000

155.000

155.000

a.Locate the range on the printout. Comment on the accuracy of the statement: 鈥淭he difference between the largest and smallest values of level of support for the 992 senior managers is 155 points.鈥�

b.Locate the variance on the printout. Comment on the accuracy of the statement: 鈥淥n average, the level of support for corporate sustainability for the 992 senior managers is 722 points.鈥�

c.Locate the standard deviation on the printout. Does the distribution of support levels for the 992 senior managers have more or less variation than another distribution with a standard deviation of 50? Explain.

d.Which measure of variation best describes the distribution of 992 support levels? Explain.

Short Answer

Expert verified
  1. Range = 155, Statement = Accurate
  2. Variance = 722.036, Statement = Not accurate
  3. Standard deviation = 26.871, Less variation
  4. Standard Deviation

Step by step solution

01

Locating the range and commenting on the statement 

The range mentioned in the printout is 155 points.

The range is the difference between the maximum and the minimum value in the data set. Therefore, the statement,鈥淭he difference between the largest and smallest values of level of support for the 992 senior managers is 155 points,鈥� is absolutely accurate.

02

Finding the variance and analyzing the statement 

Variance = 722.036.

Variance indicates the spread of the data, i.e., how far the data is scattered.The statement, 鈥淥n average, the level of support for corporate sustainability for the 992 senior managers is 722 points,鈥� indicates that 722 is the mean, but we know that 722 is the variance.

Therefore, the statement is not accurate.

03

Looking for the standard deviation  

The standard deviation is 26.871.

The distribution of support levels for the 992 senior managers has less variationthan another distribution with a standard deviation of 50. Standard deviation gives us an idea on far the data deviates (moves away) from the mean or the center. The higher the value of standard deviation, the higher is the variability and vice versa.

As 50 is greater than 26.871,there is less variability in the distribution of our data set compared to any other distribution with a standard deviation of 50.

04

Identifying the best measure of variation

The range here is not very helpful because it does not give us any new information as the minimum value is 0 and the maximum value is 155 itself.

The value of variance is very high, making it difficult to interpret it practically.

Therefore, Standard deviation is the best measure of variationbecause it precisely tells us how far the data is spread out from the mean, and it is also easy to interpret it practically.

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