Lesson 14

Comparing Mean and Median

Let's compare the mean and median of data sets.

Problem 1

Here is a dot plot that shows the ages of teachers at a school.

Which of these statements is true of the data set shown in the dot plot?

A:

The mean is less than the median.

B:

The mean is approximately equal to the median.

C:

The mean is greater than the median.

D:

The mean cannot be determined.

Problem 2

Priya asked each of five friends to attempt to throw a ball in a trash can until they succeeded. She recorded the number of unsuccessful attempts made by each friend as: 1, 8, 6, 2, 4. Priya made a mistake: The 8 in the data set should have been 18.

How would changing the 8 to 18 affect the mean and median of the data set?

A:

The mean would decrease and the median would not change.

B:

The mean would increase and the median would not change.

C:

The mean would decrease and the median would increase.

D:

The mean would increase and the median would increase.

Problem 3

In his history class, Han's homework scores are:

100

100

100

100

95

100

90

100

0

The history teacher uses the mean to calculate the grade for homework. Write an argument for Han to explain why median would be a better measure to use for his homework grades.

Problem 4

The dot plots show how much time, in minutes, students in a class took to complete each of five different tasks. Select all the dot plots of tasks for which the mean time is approximately equal to the median time.

Here is a set of coordinates. Draw and label an appropriate pair of axes and plot the points. $$A = (1, 0)$$, $$B = (0, 0.5)$$, $$C= (4, 3.5)$$, $$D = (1.5, 0.5)$$