Mean, Median, Mode & Range Cheat Sheet

A printable reference covering mean, median, mode, range, data ordering, and outliers for grades 5-8.

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Statistics helps students describe a set of numbers using simple summary values. This cheat sheet covers mean, median, mode, and range, which are common measures used to understand data. Students need these tools to compare groups, read graphs, and make sense of real-world information like test scores, temperatures, and survey results. A clear reference makes it easier to remember when and how to use each measure. The mean is found by adding all values and dividing by the number of values. The median is the middle value after the data are placed in order, while the mode is the value that appears most often. The range shows how spread out the data are by subtracting the smallest value from the largest value. Outliers can affect some statistics, especially the mean and range, so they should always be noticed.

Key Facts

The mean is the average and is found using $\text{mean} = \frac{\text{sum of all values}}{\text{number of values}}$ .
To find the median, first order the data from least to greatest, then choose the middle value.
If there are two middle values, the median is their average: $\text{median} = \frac{\text{middle value 1} + \text{middle value 2}}{2}$ .
The mode is the value that appears most often, and a data set can have one mode, more than one mode, or no mode.
The range measures spread and is found using $\text{range} = \text{maximum} - \text{minimum}$ .
An outlier is a value that is much greater or much less than most of the other values in a data set.
The mean is sensitive to outliers because every value is included in the sum.
The median is often a better measure of center when a data set has an extreme outlier.

Vocabulary

Mean: The mean is the average of a data set, found by dividing the sum of the values by the number of values.
Median: The median is the middle value of a data set after the values are arranged from least to greatest.
Mode: The mode is the value or values that occur most often in a data set.
Range: The range is the difference between the greatest value and the least value in a data set.
Outlier: An outlier is a data value that is far away from most of the other values.
Data Set: A data set is a collection of numbers or observations used for analysis.

Common Mistakes to Avoid

Finding the median before ordering the data is wrong because the middle value only makes sense after the numbers are placed from least to greatest.
Dividing by the wrong number when finding the mean is wrong because $\text{mean} = \frac{\text{sum}}{\text{number of values}}$ , not the largest value or the range.
Forgetting to average the two middle values in an even-sized data set is wrong because there is no single middle value when the number of values is even.
Choosing the largest number as the mode is wrong because the mode is the value that appears most often, not necessarily the greatest value.
Calculating range by subtracting nearby values is wrong because the range must use only the maximum and minimum: $\text{range} = \text{maximum} - \text{minimum}$ .

Practice Questions

1 Find the mean, median, mode, and range of the data set $4, 6, 6, 8, 11$ .
2 The temperatures for six days were $72, 75, 70, 80, 75, 78$ . Find the mean and mode.
3 Order the data set $15, 9, 12, 9, 20, 10$ and find its median and range.
4 A data set has one very large outlier. Explain whether the mean or median would better represent a typical value and why.

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