KS3

Calculating the mean, mode and range from a frequency table

Part ofMathsAverages

Key points

An image of counters to represent raw data. The data has been represented in a table. — Image caption,
Frequency tables can be used to help present sets of data.

A set of data can be presented in a table instead of a long list of numbers. A frequency table shows how many times a value occurs.
To find the sum of all the values, multiply each category by its frequency and then find the total of the results. The sum of all the frequencies shows how many values there are. The mean is the sum of all the values divided by how many values there are.
The from a frequency table is the value that has the highest frequency.
The measures how spread out the data is. It is the difference between the lowest and highest value.

An image of counters to represent raw data. The data has been represented in a table. — Image caption,
Frequency tables can be used to help present sets of data.

How to find the mean from a frequency table

The from a list is calculated by adding all the values and dividing by how many values there are. When data is shown in a frequency table, these figures are found by carrying out calculations using the rows and columns.
To find the mean from a frequency table:
1. Set up a new column to multiply each category by its frequency.
2. Find the sum of the new column. This finds the total of all the values in the frequency table.
3. Add the frequencies to find how many values there are.
4. Divide the total of all the values by how many values there are.

Examples

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Image caption,
Each circle represents a child who attended a summer school, along with their age.
Image caption,
The same data is presented in a frequency table. The frequency column shows how many children are each age. For example, there are 4 ten-year-olds, so the frequency for age 10 is 4
Image caption,
There are 4 children aged 10, which gives a total age of 40 in that category. There are 6 children aged 11, which gives a total age of 66 in that category. There are 3 children aged 12, which gives a total age of 36 in that category. There are 2 children aged 13, which gives a total age of 26 in that category.
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There are 15 children altogether. Using the frequency table, the number of children is the total of all the frequencies.
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To find the mean age, use a calculator to divide the total age of all the children (168) by how many children there are (15). 168 ÷ 15 = 11.2. The mean age is 11.2 years old.
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The table shows how many potatoes are in 10 bags. Calculate the mean number of potatoes in a bag.
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There are 2 bags with 7 potatoes in. These bags contain 7 x 2 = 14 potatoes in total. There are no bags with 8 potatoes in. There are 4 bags with 9 potatoes in. These bags contain 9 x 4 = 36 potatoes in total. Make a new column to write in the results of all the multiplications.
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Add the figures in the new column to find the total number of potatoes in all the bags. 14 + 0 + 36 + 30 + 11 = 91
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Add all the frequencies to find the number of bags. This may also be given in the question. There are 10 bags.
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To calculate the mean, divide the total number of potatoes in all the bags (91) by how many bags there are (10). 91 ÷ 10 = 9.1. The mean number of potatoes in a bag is 9.1

Questions

1. Finding the mode

The table shows the star rating for 20 hotels.

What is the mode star rating?

An image of a table. The table has two columns and six rows. The first column is labelled, star rating, and is populated with the numbers, one, two, three, four and five. The second column is labelled frequency and is populated with the numbers, three, eight, four, three, and two.

2. Finding the range

The table shows the shoe sizes of a class of students.

What is the range?

An image of a table. The table has two columns and six rows. The first column is labelled, shoe size, and is populated with the numbers, three, four, five, six and seven. The second column is labelled frequency and is populated with the numbers, five, eight, nine, five, and one.

Practise working out mean, mode and range from a frequency table

Practise working out mean, mode and range from a frequency table with this quiz. You may need a pen and paper to help you with your answers.

Quiz

Real-life maths

An image of a satisfaction rating, ranging from one to five stars. — Image caption,
Companies can use frequency tables to group customer rates of services and products.

Data obtained from customer satisfaction surveys can often contain hundreds or thousands of values. Presenting the data as a table makes it much easier to analyse and make conclusions.

Calculating and ranges from survey data gives insight into the overall satisfaction level of customers. By identifying areas where satisfaction is high or low, companies can make data-driven decisions to improve their products or services.

An image of a satisfaction rating, ranging from one to five stars. — Image caption,
Companies can use frequency tables to group customer rates of services and products.

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