Question

Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 ( p. 83). Recall that level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each of 992 senior managers at CPA firms. Numerical measures of central tendency for level of support are shown in the accompanying Minitab printout.

Descriptive Statistics: Support
Variable Support	N	Mean	Minimum	Median	Maximum	Mode	N for mode
992	67.755	0.000	68.000	155.000	64	20

a.Locate the mean on the printout. Comment on the accuracy of the statement: “On average, the level of support for corporate sustainability for the 992 senior managers was 67.76 points.”

b.Locate the median on the printout. Comment on the accuracy of the statement: “Half of the 992 senior managers reported a level of support for corporate sustainability below 68 points.”

c.Locate the mode on the printout. Comment on the accuracy of the statement: “Most of the 992 senior managers reported a level of support for corporate sustainability below 64 points.”

d.Based on the values of the measures of central tendency, make a statement about the type of skewness (if any) that exists in the distribution of 992 support levels. Check your answer by examining the histogram shown in Exercise 2.23.

Short answer

a) Mean = 67.755

b) Median = 68.000

c) Mode = 64

d) Symmetric

Step-by-step solution

Locating the mean and commenting on it

The mean is the average of all the observations. In the given example, the mean is 67.755.

The statement, “On average, the level of support for corporate sustainability for the 992 senior managers was 67.76 points,” is accuratebecause 67.76 points are the mean level of support for corporate sustainability.

Finding the Median and interpreting it

The median is the centermost value of the observation.In the above example, the median value is 68 points.

The accuracy of the statement, “Half of the 992 senior managers reported a level of support for corporate sustainability below 68 points,” is high because, as 68 is the midpoint of the data set, 496 senior managers will have reported values above 68 and the other half of the senior managers will have reported values below 68.

Identifying the mode and Understanding it

Mode is the highly repeated value in the observations.The statement, “Most of the 992 senior managers reported a level of support for corporate sustainability below 64 points,” is not accurate.

To begin with, the mode is 64, which means that, between the rating scales of 0 to 160, the highly chosen value (20 times) by the senior managers is 64. All the other values from the scale were chosen less than 20 times.

In addition, 64 is not the median. As a result, it is impossible for half of the 992 managers to have picked a number less than 64.

Checking for skewness

Skewness can be identified by looking at the mean and the median. As we can see that the mean and the median are both very close to each other, we can say that there is no skewness. The distribution is symmetric.