The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Averages from Grouped Data

In this worksheet, students read grouped data from frequency tables in order to work out the mean, median and mode.

'Averages from Grouped Data' worksheet

Key stage:  KS 3

Curriculum topic:  Statistics

Curriculum subtopic:  Understand Variables, Representation, Measures and Spread

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Data organised in a frequency table can be used to work out the mean, median and mode.

The number of items in the group can be found by adding up the frequencies.  

Remember that "frequency" is just "how many times" something occurs.

When data is grouped, the exact value is not known.

 

Example

This table shows the masses of children in a year 9 class at school.

Find the mean, median and mode.

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 3
 60 ≤ m < 65 1

 

This means that:

2 children have a mass greater than or equal to 40 kg but less than 45 kg.

5 children have a mass greater than or equal to 45 kg but less than 50 kg ..... etc.

  

Mean

We have to estimate the mean by using the midpoint value in each class.

These are 42.5, 47.5, 52.5, 57.5 and 62.5 kg

 

The total mass of all the children is (2 x 42.5) + (5 x 47.5) + (9 x 52.5) + (3 x 57.5) + (1 x 62.5) = 1030 kg

 

There are 2 + 5 + 9 + 3 + 1 = 20 children in the class.

 

Mean mass = 1030 ÷ 20 = 51.5 kg

 

Median

There are 20 children, so the "middle person" will be the 10th and 11th.

The 10th and 11th person falls into the 50 ≤ m < 55 class

The median class is 50 ≤ m < 55 kg

 

Mode

This is the class with the highest frequency.

The modal class is  50 ≤ m < 55 kg

This table shows the masses of children in a year 9 class at school.

Find the modal class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

40 ≤ m < 45

45 ≤ m < 50

50 ≤ m < 55

55 ≤ m < 60

60 ≤ m < 65

This table shows the masses of children in a year 9 class at school.

Find the median class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

40 ≤ m < 45

45 ≤ m < 50

50 ≤ m < 55

55 ≤ m < 60

60 ≤ m < 65

This table shows the masses of children in a year 9 class at school.

Estimate the total mass of all the children in kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

This table shows the masses of children in a year 9 class at school.

Estimate the mean mass of all the children to the nearest kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

This table shows the masses of children in a year 9 class at school.

Find the modal class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

40 ≤ m < 45

45 ≤ m < 50

50 ≤ m < 55

55 ≤ m < 60

60 ≤ m < 65

This table shows the masses of children in a year 9 class at school.

Find the median class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

40 ≤ m < 45

45 ≤ m < 50

50 ≤ m < 55

55 ≤ m < 60

60 ≤ m < 65

This table shows the masses of children in a year 9 class at school.

Estimate the total mass of all the children in kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

This table shows the masses of children in a year 9 class at school.

Estimate the mean mass of all the children to the nearest kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

This table shows the masses of children in a year 9 class at school.

Estimate the total mass of all the children in kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 9
 50 ≤ m < 55 6
 55 ≤ m < 60 7
 60 ≤ m < 65 5

 

This table shows the masses of children in a year 9 class at school.

Estimate the mean mass of all the children to the nearest kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 9
 50 ≤ m < 55 6
 55 ≤ m < 60 7
 60 ≤ m < 65 5

 

  • Question 1

This table shows the masses of children in a year 9 class at school.

Find the modal class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

CORRECT ANSWER
55 ≤ m < 60
  • Question 2

This table shows the masses of children in a year 9 class at school.

Find the median class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

CORRECT ANSWER
50 ≤ m < 55
  • Question 3

This table shows the masses of children in a year 9 class at school.

Estimate the total mass of all the children in kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

CORRECT ANSWER
1490
EDDIE SAYS
(2 x 42.5) + (5 x 47.5) + (9 x 52.5) + (11 x 57.5) + (1 x 62.5) = 1490
  • Question 4

This table shows the masses of children in a year 9 class at school.

Estimate the mean mass of all the children to the nearest kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 2
 45 ≤ m < 50 5
 50 ≤ m < 55 9
 55 ≤ m < 60 11
 60 ≤ m < 65 1

 

CORRECT ANSWER
53
EDDIE SAYS
1490 ÷ 28 = 53.2
  • Question 5

This table shows the masses of children in a year 9 class at school.

Find the modal class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

CORRECT ANSWER
50 ≤ m < 55
  • Question 6

This table shows the masses of children in a year 9 class at school.

Find the median class.

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

CORRECT ANSWER
50 ≤ m < 55
  • Question 7

This table shows the masses of children in a year 9 class at school.

Estimate the total mass of all the children in kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

CORRECT ANSWER
1295
EDDIE SAYS
(3 x 42.5) + (2 x 47.5) + (8 x 52.5) + (7 x 57.5) + (4 x 62.5) = 1295
  • Question 8

This table shows the masses of children in a year 9 class at school.

Estimate the mean mass of all the children to the nearest kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 2
 50 ≤ m < 55 8
 55 ≤ m < 60 7
 60 ≤ m < 65 4

 

CORRECT ANSWER
54
EDDIE SAYS
1295 ÷ 24 = 53.958
  • Question 9

This table shows the masses of children in a year 9 class at school.

Estimate the total mass of all the children in kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 9
 50 ≤ m < 55 6
 55 ≤ m < 60 7
 60 ≤ m < 65 5

 

CORRECT ANSWER
1585
EDDIE SAYS
(3 x 42.5) + (9 x 47.5) + (6 x 52.5) + (7 x 57.5) + (5 x 62.5) = 1585
  • Question 10

This table shows the masses of children in a year 9 class at school.

Estimate the mean mass of all the children to the nearest kg.

(Just write the number)

 

 Mass (m kg) Frequency
 40 ≤ m < 45 3
 45 ≤ m < 50 9
 50 ≤ m < 55 6
 55 ≤ m < 60 7
 60 ≤ m < 65 5

 

CORRECT ANSWER
53
EDDIE SAYS
1585 ÷ 30 = 52.8
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1