Question

1. The following data from several years ago represent salaries (in dollars) from a school district in Greenwood, South Carolina. 10, 000 11, 000 11, 000 12, 500 14, 300 17, 500 18, 000 16, 600 19, 200 21, 560 16, 400 107, 000 (a) First, assume you work for the school board in Greenwood and do not wish to raise taxes to increase salaries. Compute the mean, median, and mode and decide which one would best support your position not to raise salaries. (b) Second, assume you work for the teachers union and want a raise for the teacher. Use the best measure of central tendency to support your position. (c) Explain how outliers can be used to support one or the other position. (d) If the salaries represented every teacher in the school district, would the averages be parameters or statistics? (e) Which measure of the central tendency can be misleading when a data set contains outliers? (f) When you are comparing the measures of central tendency, does the distribution display any skewness? Explain

Answer 1

(a) First, assume you work for the school board in Greenwood and do not wish to raise taxes to increase salaries. Compute the mean, median, and mode and decide which one would best support your position not to raise salaries.

Here,

Mean = 22921.67

This is calculated by using excel command as =AVERAGE()

Median = 16500

This is also calculated by using excel command as =MEDIAN()

Mode = 11000

This is also calculated by using excel command as =MODE()

If you work for the school board and do not want to raise salaries, you could say that the average teacher salary is 22,921.67.

(b) Second, assume you work for the teachers union and want a raise for the teacher. Use the best measure of central tendency to support your position.

If you work for the teachers’ union and want a raise for the teachers, either the sample median of 16,500 or the sample mode of 11,000 would be a good measure of center to report.

(c) Explain how outliers can be used to support one or the other position.

The outlier is 107,000. With the outlier removed, the sample mean will be 15,278.18, the sample median is 16,400, and the sample mode is still 11,000. The mean is greatly affected by the outlier and allows the school board to report an average teacher salary that is not representative of a “typical” teacher salary.

(d) If the salaries represented every teacher in the school district, would the averages be parameters or statistics?

If the salaries represented every teacher in the school district, the averages would be parameters, since we have data from the entire population.

(e) Which measure of the central tendency can be misleading when a data set contains outliers?

. The mean can be misleading in the presence of outliers, since it is greatly affected by these extreme values.

(f) When you are comparing the measures of central tendency, does the distribution display any skewness? Explain

Since the mean is greater than both the median and the mode, the distribution is skewed to the right (positively skewed).