Mean Absolute Deviation Another useful measure of variation for a data set is the mean absolute deviation (MAD). It is calculated by the formula
MAD = Σ |x − x̄| / n.
b. Find the mean absolute deviation of the data set in Exercise 16. Compare your result with the sample standard deviation obtained in Exercise 16.

Refer to the sample statistics from Exercise 5 and determine whether any of the house prices below are unusual. Explain your reasoning.

d. $147,000

Using the Empirical Rule In Exercises 29–34, use the Empirical Rule.

Use the sample statistics from Exercise 29 and assume the number of vehicles in the sample is 75.

a. Estimate the number of vehicles whose speeds are between 63 miles per hour and 71 miles per hour.

Use frequency distribution formulas to estimate the sample mean and the sample standard deviation of the data set in Exercise 2.

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.

40   35   49   53   38   39   40

37   49   34   38   43   47   35

c. Each employee in the sample takes a pay cut of $2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set.

Scaling Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.

42   36   48   51   39   39   42

36   48   33   39   42   45   50

b. Each employee in the sample receives a 5% raise. Find the sample mean and the sample standard deviation for the revised data set.

Extending Concepts

Alternative Formula You used SSₓ = Σ(x − x̄)² when calculating variance and standard deviation. An alternative formula that is sometimes more convenient for hand calculations is

SSₓ = Σ x² − (Σ x)² / n.

You can find the sample variance by dividing the sum of squares by n − 1 and the sample standard deviation by finding the square root of the sample variance.

b. Use the alternative formula to calculate the sample standard deviation for the data set in Exercise 15.

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.

40   35   49   53   38   39   40

37   49   34   38   43   47   35

a. Find the sample mean and the sample standard deviation.

Constructing Data Sets In Exercises 25–28, construct a data set that has the given statistics.

N = 6

μ = 5

σ ≈ 2