Calculate mean, median, mode, and range

For a finite numerical data set, the mean is the total divided by the number of values and represents an equal-share balance point; the median is the middle value when data are ordered (or the mean of the two middle values), the mode is the most frequent value and may be absent or nonunique, and the range is maximum minus minimum. Interpretation includes comparing how these measures describe center and spread and recognizing that extreme values affect the mean and range more than the median. This scope excludes weighted means, grouped-data estimates, and inferential statistics.

Detailed Explanation: Calculate mean, median, mode, and range

For a data set, use these steps:

Mean: Add all values and divide by the number of values.
Median: Put the values in order. Find the middle value. If there are two middle values, find their mean.
Mode: Find the value that occurs most often. There may be no mode or more than one mode.
Range: Subtract the smallest value from the largest value.

Example

A group of students records the number of minutes they read:

4,\ 6,\ 6,\ 7,\ 9,\ 12

The data are already in order.

1. Find the mean

Add the values:

4+6+6+7+9+12=44

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

\text{Mean}=\frac{44}{6}=7\frac{1}{3}\approx 7.3

The mean reading time is about $(7.3)$ minutes.

2. Find the median

There are $6$ values, so there are two middle values: $6$ and $7$ .

Find their mean:

\text{Median}=\frac{6+7}{2}=6.5

The median is $(6.5)$ minutes.

3. Find the mode

The value $6$ occurs twice, while every other value occurs once.

\text{Mode}=6

4. Find the range

Subtract the smallest value from the largest value:

\text{Range}=12-4=8

The range is $8$ minutes.

The mean and median describe the center of the data. The mode shows the most common value, and the range describes the spread from the smallest to the largest value. An unusually large or small value affects the mean and range more than it affects the median. Here, the value $(12)$ increases the mean and the range, but the median is less affected.

Learn by doing: Calculate mean, median, mode, and range

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Statistics - Solve for Mean

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