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GCSE Maths Statistics

Mean, median, mode

Mean, Median, Mode

Here we will learn about the mean, median and mode, including what they are and how to find them.

There are also mean median mode worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is mean median mode?

The mean, median and mode are averages.

Averages are measures of central tendency, they are values that can be used to represent a set of data.

We will look at three averages: mean, median and mode.

See also: Range

What is mean median mode?

Mean

To calculate the mean we find the total of the values and divide the total by the number of values.

The “number of values” is sometimes referred to as the “number of numbers”.

\text{Mean}=\frac{\text{total}}{\text{number of values}}

E.g. Find the mean of this set of numbers

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{1+3+4+5+6+6+7}{7}=\frac{32}{7}=4.57 \ \text{(to 2 dp)}

The mean is $4.57$ (to $2 dp$ ).

Step-by-step guide: Mean

Median

The median is the middle number.

To find the median we need to arrange the values in numerical order, from the smallest value to the highest value and find the middle value.

The middle value is the median value.

E.g. Find the median of this set of numbers

The median is $5$ .

Step-by-step guide: Median

Mode

The mode is the most common number.

To find the mode we need to find the most frequently occurring item in the data set.

E.g. Find the mode of this list of numbers

The most frequently occurring item is $‘6’$

The mode is $6$ .

Step-by-step guide: Mode or modal

How to find the mean median mode

In order to find the mean, median or mode:

Mode – consider how many times the values occur; there may be two modes (bimodal).
Median – make sure the list of values is in numerical order, and find the middle of the set.
Mean – find the total and divide by the number of values.

How to find the mean median mode

Mean median mode worksheet

Get your free mean median mode worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Mean median mode worksheet

Get your free mean median mode worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Mean median mode examples

Example 1: finding the mode

Find the mode:

Consider the number of times the different items occur.

$7$ occurs twice, more than any other item.

The mode is $7$

Example 2: finding the mode

Find the mode:

Consider the number of times the different items occur.

$3$ and $6$ both occur twice so there are two modes. The data is bimodal.

The mode is $3$ and $6$

Example 3: finding the median

Find the median:

Make sure the list of numbers is in numerical order.

Find the middle of the data set.

The median is $9$

Example 4: finding the median

Find the median:

Make sure the list of numbers is in numerical order.

Find the middle of the data set. There is an even number of values, so we have a middle pair. The average of $4$ and $6$ is $5$ . (Or the midpoint of $4$ and $6$ is $5$ ).

\frac{4+6}{2}=\frac{10}{2}=5

The median is $5$

Example 5: finding the mean

Find the mean:

Find the total and divide by the number of values

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{7+8+6+8+9}{5}=\frac{38}{5}=7.6

The mean is $7.6$

Example 6: finding the mean

Find the mean:

Find the total and divide by the number of values

\text{Mean}=\frac{\text{total}}{\text{number of values}}=\frac{11+13+16+12+12+14}{6}=\frac{78}{6}=13

The mean is $13$

Common misconceptions

Mixing up the averages

Check if you have been asked for the median, mode or mean average.

No mode?

A data set can have $1$ mode or $2$ modes (bimodal) etc. But it is possible that a data set has no mode at all.

Ascending order

Check that the list of numbers is in numerical order before finding the median number.

Decimal averages

The mean does not have to be a whole number. It can be a decimal or a fraction. It may be a decimal which needs rounding.

Practice mean median mode questions

12

17

18

16

The most common item is $‘18’$ . The number of times $‘18’$ occurs is $2$ times. The other numbers only occur once.

19

21

23

$19$ and $23$

The most common items are $‘19’$ and $‘23’$ . These two items occur twice. The other numbers only occur once.

18

19

17

31

Put the numbers in order from the smallest to largest value. Then find the middle value.

The middle value is $17$ , so this is the median.

35

36

37

38

Put the numbers in order from the smallest to largest value. Then find the middle value.

The middle pairs of values are $35$ and $37$ . The average of these is $36$ . The median is $36$ .

\frac{35+37}{2}=\frac{72}{2}=36

17

12.5

16.4

15.5

\text{Mean}= \frac{\text{total}}{\text{number of values}}

\text{Mean}=\frac{18+12+15+17}{4}

\text{Mean}= \frac{62}{4}

\text{Mean}=15.5

6

8

7

5

\text{Mean}= \frac{\text{total}}{\text{number of values}}\\ \text{Mean}=\frac{7+8+6+4+9+7+1}{7}\\ \text{Mean}= \frac{42}{4}\\ \text{Mean}=6

Mean median mode GCSE questions

1. Here is a list of numbers

(a) Write down the mode
(b) Work out the median
(c) Work out the mean

(4 marks)

Show answer

(a)

$15$
For the correct answer

(1)

(b)

$16$
For the correct answer

(1)

(c)

$(18+15+19+16+15)\div 5$
For adding the numbers and dividing by $5$

(1)

$=\frac{83}{5}=16.6$
For the correct answer

(1)

2. Here is a list of numbers

(a) Write down the mode
(b) Work out the median
(c) Work out the mean

(5 marks)

Show answer

(a)
$1.4$
For the correct answer

(1)

(b)
$1.2 1.4 1.4 1.6 1.8 1.9 2.0$
For putting the numbers in order

(1)

$1.6$
For the correct answer

(1)

$=\frac{11.3}{7}=1.6142…=1.61 \ \text{(to 3 sf)}$
For the correct answer

(1)

3. There are five cards with some numbers on them.
The number on one of the cards is $2$ .

The mean of $5$ numbers is $7$ .
The mode is $10$ .
The median is $8$ .

Find the numbers on the other four cards.

(4 marks)

Show answer

$10$ and $10$
For using the mode to write that $2$ cards are $10$

(1)

$8$
For using the median to write that $1$ card is $8$

(1)

$(7\times 5)-(2+8+10+10)$
For using the mean to find the total of the cards and subtracting the sum of the other cards

(1)

$=5$
For the correct answer

(1)

Learning checklist

You have now learned how to:

Find the mode

Find the median

Calculate the mean (also known as the arithmetic mean)

The next lessons are

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