Question

1. For each of the following situations, determine which measure of central tendency is most appropriate and justify your

reasoning.

a. Average test score when the scores are skewed left

b. Average price of a home sold in Pittsburgh, Pennsylvania, in 2015

c. Most popular major for students enrolled in a statistics course

2. Use the five test scores of 65, 70, 71, 75, and 95 to answer the following questions:

1. Which measure of central tendency better describes the typical test score and why?
2. What effect does adding (or subtracting) a constant has on the measures of central tendency? Explain.

Answer 1

1

(a)

Average test score when the scores are skewed left

measure of central tendency is most appropriate = Median

Justification: Median is not affected by extreme values, whereas mean and mode are affected by extreme values.

(b)

Average price of a home sold in Pittsburgh, Pennsylvania, in 2015

measure of central tendency is most appropriate = Median

Justification: Distribution of price of a home is highly skewed. Median is not affected by extreme values, whereas mean and mode are affected by extreme values.

(c)

Most popular major for students enrolled in a statistics course

measure of central tendency is most appropriate = Mode

Justification:Mode corresponds to the maximum occurrence.

2.

(a)

Mean measure of central tendency better describes the typical test score. Mean = 376/5 = 75.2

Reason: There is o outlier in the data set. So,mean is appropriate measure of central tendency.

(b)

By adding a constant, all the 3 measures of central tendency: viz;, mean, median and mode will increase by that constant.

By subtracting a constant, all the 3 measures of central tendency: viz;, mean, median and mode will decrease by that constant.