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How to find the mean, median, mode and range?

2nd October, 2022

How to find the mean, median, mode and range

Mean, Mode and Median are all types of averages. The average of a set numbers is never bigger than the biggest number, or smaller than the smallest, but a number somewhere in between.

The range is not an average, but it is the difference between the largest and the smallest number in a set of numbers.

How to find the mean of a set of numbers

One type of average. You find the mean by adding all the numbers together and dividing by the number of numbers.

How to find the mean

e.g. “find the mean of the three numbers 2, 4 and 6

Adding 2, 4 and 6 gives 12

12 divided by 3 equals 4

therefore “the mean of 2, 4 and 6 is 4

It is “MEAN” because you have to do the most work of all the averages!

How to find the median of a set of numbers

One type of average. You find the meDian of a set of numbers by first putting the numbers in numerical order, and then find the number in the miDDle of that set.

How to find the median

e.g. “find the median of 1, 5 and 9

The numbers are already in numerical order: 1, 5, 9

The middle number is 5.

therefore “the median of 1, 5 and 9 is 5

 

e.g. “find the median of 5, 2, 4 and 8

Put the numbers into numerical order: 2, 4, 5, 8

There are two middle numbers: 4 and 5, so find the number that is halfway between 4 and 5

The number that is halfway between 4 and 5 is 4.5.

therefore “the median of 5, 2, 4 and 8 is 4.5

How to find the mode of a set of numbers

One type of average. You find the MOde of a set of numbers by looking for number that appears the MOst.

How to find the mode

e.g. “find the mode of the numbers 3, 6, 3, 9, 3

There are three 3s, one 6 and one 9, so the number 3 appears the most.

therefore “the mode of the numbers 3, 6, 3, 9, 3 is 3

How to find the range of a set of numbers

The range is not an average, but it is the difference between the largest and the smallest number in a set of numbers. You subtract the smallest number from the largest to find the range.

How to find the range

e.g. “find the range of the numbers 1, 2, 5, 4, 9 and 7

The largest number is 9 and the smallest is 1.

9 minus 1 is 8

therefore “the range of the numbers 1, 2, 5, 4, 9 and 7 is 8

Printable revision guide on How to find the mean, median, mode and range

How to find the mean, median, mode and range
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My name is Nicola Bhalerao and I am a private tutor based in Warwick. Since 2013, I have provided one-to-one tuition for children and adults. I specialise in maths tutoring, but cater for different requests, ranging from 11+ to various computing skills, including website training.

My background is in computing, with a Computer Science degree from Warwick University. I have worked many years as a programmer, latterly in the games industry. Both my sons were tutored by me for the 11+ (they went to a local grammar school). I received training for teaching secondary school maths and I am fully CRB checked.

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