Question

Please complete the following problem.

Creating Data Sets

NINE students kept track of how many hours they played sports during August. Their mean was 24 hours. How many hours might each of the students have played sports? Your challenge is to make data sets to match the descriptions below. You MAY use a calculator for this activity.

• Create a different data set to match each of the conditions listed below.

• Please circle the median of each set and put a square around the mode, if any.

i. Mean is larger than the median:

ii. Median is larger than the mean:

iii. Mode is larger than the mean:

iv. Mean is larger than the mode:

v. Mode is larger than the median:

vi. Median is larger than the mode:

vii. Mean, median, and mode are equal, but every student did not play the same number of hours:

Answer 1

Mean: The average value of the data

Median: The middle value of the data. In this case the value of the 5th data point when the data set is arranged in ascending or descending order.

Mode: The value which occurs the highest number of times

Example:

Consider the first data set:

12, 14, 16, 18, 20, 30, 30, 36, 40

In this case,

Mean = Average = (12+14+16+18+20+30+30+36+40)/9 = 216/9 = 24

The data set is aranged in ascending order.

Hence, Median = Value of 5th data point = 20

In this case, 30 appears twice while all other values appear only once.

Hence, Mode = 30

Note: In each data set, median is circled and mode values are kept in square boxes.