Use measures of center in context

Detailed Explanation: Use measures of center in context

A measure of center gives one number that represents a data set. The three common measures are:

• Mean: Add all the values and divide by how many values there are. It shows the equal-share value.
• Median: Put the values in order and find the middle. If there are two middle values, find their mean.
• Mode: Find the value that occurs most often.

Example: Six students recorded how many minutes they read one evening:

The values are already in order.

1. Find the mean.

Add the minutes:

There are $6$ values, so divide by $6$:

The mean is $80$ minutes. If the total reading time were shared equally among the six students, each student would have read for $80$ minutes.

2. Find the median.

There are two values in the middle: $75$ and $78$. Find their mean:

The median is $76.5$ minutes. Half of the students read for at most $76.5$ minutes, and half read for at least $76.5$ minutes.

3. Find the mode.

The value $75$ occurs twice. Every other value occurs once.

The mode is $75$ minutes.

Compare the measures.

• Mean: $80$ minutes
• Median: $76.5$ minutes
• Mode: $75$ minutes

The $100$-minute value is much higher than the other values, so it pulls the mean upward. Most of the reading times are between $72$ and $80$ minutes, so the median of $76.5$ minutes may better describe a typical student’s reading time. The mode tells us that $75$ minutes was the most common amount.