Select an appropriate measure of centre

Detailed Explanation: Select an appropriate measure of centre

A measure of centre describes a typical value in a data set. Choose the measure that best represents the data:

• Mean: Add all values and divide by the number of values. It uses every value, so extreme values can affect it.
• Median: Put the values in order and find the middle value. It is usually a better choice when there is an extreme value.
• Mode: Find the value that occurs most often. It is useful when the most common value or category matters.

Example

A group of students records the number of minutes they spent reading last night:

Step 1: Look for unusual values.

The value $120$ is much larger than the other values. It is an extreme value.

Step 2: Find the mean.

The mean is about $42.1$ minutes. However, most students read between $20$ and $40$ minutes, so the mean has been pulled higher by the $120$ minutes.

Step 3: Find the median.

The values are already in order. There are $7$ values, so the middle value is the fourth value:

Step 4: Choose the most appropriate measure.

The median, $30$ minutes, is the best measure of centre because the data contain an extreme value. It gives a more typical reading time for the group than the mean.

When choosing a measure of centre, check for extreme values, look at what occurs most often, and think about what “typical” should mean for the data.