Alicia received the following seven scores on her math assignments. 80, 90, 10, 75, 90, 95, 99

Find the mean and median. Which measure of center best represents the data?

Answers:

Explanation:

Part (1) Finding the mean

Add up the values to get

80 + 90 + 10 + 75 + 90 + 95 + 99 = 539

Then divide by 7 because there are 7 values in this list

539/7 = 77

The mean is 77

Part (2) Finding the median

First we'll need to sort the values from smallest to largest

{80, 90, 10, 75, 90, 95, 99}

will sort to

{10, 75, 80, 90, 90, 95, 99}

The middle most value is 90 since we have three items below it {10,75,80} and three items above it {90, 95, 99}.

The median is 90

Part (3) Which is the better measure of center?

Nearly all of the values are clustered from 75 to 99. The value 10 is an outlier since it's far from the main cluster. There are more technical processes used to find out if 10 is actually an outlier or not, but we won't deal with that right now.

The much smaller outlier pulls on the mean to make it smaller than what it should be. The mean 77 is too small to represent what the center should be. The median is not affected by outliers, which is why it's used in applications such as home prices.

The median 90 is the better measure of center.