Chapter overview Maths

Exam board

AQA

Number

Algebra

Graphs

Ratio proportion and rates of change

Shapes and area

Angles and geometry

Trigonometry

Probability

Statistics

Maths

# Frequency tables: finding averages 0%

Summary

# Frequency tables: finding averages

## ​​In a nutshell

Just like for sets of values, the mean, median, mode and range can be found from frequency tables too. The only difference is that these averages might refer to a category, rather than an individual number.

#### PROCEDURE

 Mean Create a new column: 'number $\times$ frequency' and calculate these values. Next, find the sum of all these values, then divide this number by the total frequency. Median Identify the category containing the middle value: use $\frac{n+1}{2}$ where n is the total frequency to find the middle position. Mode Identify the category with the highest frequency. Range Calculate the difference between the highest and lowest in the 'number of' column.

##### Example

This frequency table shows the number of siblings pupils in a class of $23$ have:

 Number of siblings Frequency ​$0$​​ ​$6$​​ ​$1$​​ ​$12$​​ ​$2$​​ ​$3$​​ ​$3$​​ ​$2$​​ ​$4$​​ ​$0$​​

Find the mean, median, range and mode.

1. Mean:

Add the third column to the table.

 Number of siblings $\times$ frequency ​$0\times6=0$​​​ ​$1\times12=12$​​ ​$2\times3=6$​​ ​$3\times2=6$​​ ​$4\times0=0$​​​

Use the formula:

$\frac{\text{sum of 'number}\times \text{frequency' column}}{\text{total frequency}}=\frac{12+6+6}{6+12+3+2}=\frac{24}{23}=\underline{1.043} \text{ (to 3 d.p})$​​

Note: The total number of students was given in the question here, but often you will need to calculate it yourself.

2. Median:

Identify the middle position.

$\frac{(n+1)}{2}=\frac{(23+1)}{2}=12$​​

The median is the category containing the $12th$ value cumulatively: $\underline1$

3. Mode:

Identify the category with the highest frequency.

$\underline1$

4. Range:

Work out the difference between the highest and lowest number of siblings.

$3-0 = \underline3$​​

Note: $4$ is not used here as there is no one with $4$ siblings.​

## Want to find out more? Check out these other lessons!

Averages from frequency tables

FAQs

• Question: How do I find the range from a frequency table?

Answer: To find the range from a frequency table, find the difference between the highest and lowest in the 'number of' column.

• Question: How do I find the mode from a frequency table?

Answer: The mode in a frequency table is the value of the category with the highest frequency.

• Question: How do I find the median from a frequency table?

Answer: To find the mean from a frequency table, find the category containing the middle value: use (n+1)÷2 where n is the total frequency to find the middle position.​

• Question: How do I find the mean from a frequency table?

Answer: To find the mean from a frequency table: Create a new column: 'number × frequency' and calculate these values. Next, find the sum of all these values, then divide this number by the total frequency.

Theory

Exercises