Question

4. Compare/contrast the data sets below. Which data set has a range of 9, a mean of

15, a median of 14, and a mode of 11? How do you know (show work)? Why do the
other choices fail to meet the criteria? State one reason why each of the other
choices fail.
A. 11, 11, 13, 15, 20
B. 5, 11, 14, 14, 31
C. 11, 11, 14, 19, 20
D. 6, 10, 14, 15, 15

Answer 1

Let's first find the mode of each data set.

Mode = the largest value - the smallest value.

A. 20 - 11 = 9

B. 31 - 5 = 26

C. 20 - 11 = 9

D. 15 - 6 = 9

B fails because its mode does not equal 9.

Let's find the mean of A, C, and D

The mean = the sum of all data values divided by the number of data values.

A. (11 + 11 + 13 + 15 + 20) / 5 = 14.2

C. (11 + 11 + 14 + 19 + 20) / 5 = 15

D. (6 + 10 + 14 + 15 + 15) / 5 = 12

Options A and D fail because their mean does not equal 15.

Let's find the median and mode of option C

Median = the value which falls into the middle of our data set

11, 11, 14, 19, 20 = 14

Mode = the value which appears most often

In option C, 11 appears twice and every other number appears once, therefore, 11 is the mode.