Question

The salaries received in 2018 by the some of the highest paid executives of 14 international companies (in $000s) are as follows:

2411, 1889, 1520, 1260, 980, 956, 947, 924, 899, 870, 856, 655, 700, 720

1. Compute the mean, median, range, variance, and standard deviation for these sample data.
2. Discuss which of these three measures of variability (range, variance, and standard deviation) you would prefer to use as a measure of variation.
3. Comment on the skewness of the distribution of the executives’ compensation.

Answer 1

a.

Range = 2411 - 655 = 1756

b.

range is about how much your data covers, standard deviation has to do more with how much difference there is between the scores. If all of the scores are grouped around the average, then your standard deviation will be lower.

Standard deviation is mostly preferred.

c.

if a distribution is skewed, then the mean is usually not in the middle. Notice that in this example, the mean is greater than the median. This is common for a distribution that is skewed to the right.

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