Home

Maths

Statistics

Frequency tables: finding averages

Frequency tables: finding averages

Select Lesson

Exam Board

Select an option

Explainer Video

Loading...
Tutor: Alice

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 n+12\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 2323 have:


Number of siblings

Frequency

00​​

66​​
11​​
1212​​
22​​
33​​
33​​
22​​
44​​
00​​

Find the mean, median, range and mode.


1. Mean: 

Add the third column to the table.

Number of siblings ×\times frequency
0×6=00\times6=0​​​
1×12=121\times12=12​​
2×3=62\times3=6​​
3×2=63\times2=6​​
4×0=04\times0=0​​

Use the formula:

sum of ’number×frequency’ columntotal frequency=12+6+66+12+3+2=2423=1.043 (to 3 d.p)\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.

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

The median is the category containing the 12th12th value cumulatively: 1\underline1


3. Mode: 

Identify the category with the highest frequency.

1\underline1


4. Range: 

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

30=33-0 = \underline3​​


Note: 44 is not used here as there is no one with 44 siblings.​




Create an account to read the summary

Exercises

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do I find the range from a frequency table?

How do I find the mode from a frequency table?

How do I find the median from a frequency table?

How do I find the mean from a frequency table?

Beta

I'm Vulpy, your AI study buddy! Let's study together.