What is the difference between mean and median?

The mean is the average (sum ÷ count); the median is the middle value once the data is sorted.

How do you find the mode?

Find the value that appears most often in the list. A data set can have no mode (every value is unique) or more than one (a tie for most frequent).

How do you find the range?

Subtract the smallest value from the largest.

What is standard deviation?

A measure of how spread out a data set is: find the mean, square each value's distance from it, average those (dividing by n−1 for a sample), then take the square root.

Mean, Median, Mode & Range · Grades 4–12

Mean, Median, Mode & Range Worksheets

Median is the middle, mode is the most, and that rhyme is half the battle. Data worksheets covering mean, median, mode, and range. Grade 12 adds standard deviation, a measure of how spread out a sample is.

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What it is

Mean, median, mode, and range summarise a set of numbers in different ways.

Why it matters

Summarising data is essential data literacy (from report cards to sports stats to the news) and the foundation of statistics.

How to do it

Mean: add all values and divide by how many there are.
Median: sort the values and take the middle (average the two middle if even).
Mode: the value that appears most; Range: largest minus smallest.

Examples by level

BeginnerRange of 1, 10, 7, 6, 5 =9
IntermediateRange of 13, 7, 7, 5 =8
AdvancedMedian of 6, 20, 22, 16, 6, 7, 22, 10 =13

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

Forgetting to sort before finding the median.
Confusing mean and median.
Dividing by the wrong count for the mean.
Assuming every data set has exactly one mode — some have none, and some have several.
Dividing by n instead of n−1 when finding a SAMPLE standard deviation.

Tips

Always sort before finding the median.
There can be more than one mode, or none.

For parents

Median = 'middle', Mode = 'most'. The rhyme keeps them apart.

For teachers

Give a data set with an outlier to show how it pulls the mean but not the median.

Key vocabulary

mean: the average
median: the middle value
mode: the most frequent value
range: max minus min

Frequently asked questions

What is the difference between mean and median?: The mean is the average (sum ÷ count); the median is the middle value once the data is sorted.
How do you find the mode?: Find the value that appears most often in the list. A data set can have no mode (every value is unique) or more than one (a tie for most frequent).
How do you find the range?: Subtract the smallest value from the largest.
What is standard deviation?: A measure of how spread out a data set is: find the mean, square each value's distance from it, average those (dividing by n−1 for a sample), then take the square root.

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