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Mean, Median and Mode: Three Ways to Find the Average

In one line: Mean, median and mode are three different kinds of average, each giving one number that describes a typical value in a data set (a list of numbers, such as test scores or temperatures).

Why it works

Averages let you sum up lots of numbers with just one. Sports results, weather reports, shop prices and school reports all use them. Knowing all three helps you choose the fairest one. For example, one very large number can pull the mean up a lot, but the median hardly moves. Spotting this helps you avoid being misled by statistics.

Think of it like: Imagine six friends with different numbers of sweets. The mean is what each person gets if they put all the sweets in a pile and share them out equally. The median is what the friend in the middle has after everyone lines up from fewest sweets to most. The mode is the amount of sweets that the most friends have, like the most popular answer in a class vote. (Where this breaks: The sharing picture only fits the mean, and real things cannot always be shared. A mean of 4.5 goals is fine as a number, even though no team scores half a goal. The median and mode have nothing to do with sharing. They only depend on the order of the numbers and how often each one appears.)

Worked example

A team scored these goals in 6 matches: 3, 8, 5, 8, 2, 4. Find the mean, median and mode.

  1. Mean: add all the values. 3 + 8 + 5 + 8 + 2 + 4 = 30.
  2. Divide by how many values there are. There are 6 values, so 30 ÷ 6 = 5. The mean is 5.
  3. Median: put the values in order from smallest to largest: 2, 3, 4, 5, 8, 8.
  4. There is an even number of values, so there are two middle numbers, 4 and 5. Find the number halfway between them: (4 + 5) ÷ 2 = 4.5. The median is 4.5.
  5. Mode: find the value that appears most often. 8 appears twice and every other value appears once, so the mode is 8.

Answer: Mean = 5, median = 4.5, mode = 8.

Common mistakes

  • Finding the median without putting the numbers in order first; always sort them from smallest to largest before you look for the middle.
  • Dividing by the wrong number when finding the mean; divide by how many values there are, and count any zeros as values too.
  • Picking just one of the two middle numbers when there is an even number of values; add the two middle numbers and divide by 2.
  • Saying the mode is 0 when no value repeats; instead say there is no mode, and remember a data set can have more than one mode.

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What is the mode of 3, 5, 5, 9, 2?

Questions parents ask

What year do kids learn mean, median and mode?

In England, children usually start calculating the mean in Year 6, then work with the median and mode in Years 7 and 8. In Australia, all three are taught in Year 7. In the US, they usually appear in Grade 6, with more practice in Grades 7 and 8.

How can I help my child with mean, median and mode at home?

Use real numbers from everyday life, such as daily temperatures, family members' heights or points from a board game. Ask your child to find all three averages and say which one best describes the data. A handy memory trick: Mode = Most, Median = Middle, and Mean means sharing out equally.

Which average is the best one to use?

It depends on the data. The mean uses every value but can be pulled a long way by one very large or very small number, so the median is often fairer in that case. The mode is useful for the most popular choice, such as shoe size or favourite colour, and it is the only one of the three that works for data that isn't numbers.

What is the range, and is it the same as an average?

The range is the largest value minus the smallest value, so it tells you how spread out the data is. It is not an average, but it is often taught alongside mean, median and mode. For example, the range of 2, 3, 4, 5, 8, 8 is 8 − 2 = 6.