 # Averages from Frequency Charts

In this worksheet, students read grouped data from frequency charts in order to work out the mean, median and mode. Key stage:  KS 3

Curriculum topic:   Statistics

Curriculum subtopic:   Understand Variables, Representation, Measures and Spread

Difficulty level:   ### QUESTION 1 of 10

Data organised in a frequency chart 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 chart shows the heights of children in a year 6 class at school.

Find the mean, median and mode. This means that:

0 children have a height between 110 cm and 115 cm.

1 child has a height between 115 cm and 120 cm.

3 children have a height between 120 cm and 125 cm ..... etc.

Mean

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

These are 112.5, 117.5, 122.5, 127.5, 132.5, 137.5, 142.5, 147.5 and 152.5 cm

The total estimated height of all the children is    (1 x 117.5) + (3 x 122.5) + (4 x 127.5) + (7 x 132.5) + (4 x 137.5) + (2 x 142.5) + (1 x 152.5) = 2910 cm

There are 1 + 3 + 4 + 7 + 4 + 2 + 1 = 22 children in the class.

Mean height = 2910 ÷ 22 = 132.3 cm (1 dp)

Median

There are 22 children, so the "middle person" will be the 11th and 12th.

The 11th and 12th people fall into the 130 cm to 135 cm class

The median class is 130 cm to 135cm.

Mode

This is the class with the highest frequency.

The modal class  130 cm to 135cm.

This chart shows the heights of children in a year 6 class at school.

Find the modal class. 110 cm to 115 cm

115 cm to 120 cm

120 cm to 125 cm

125 cm to 130 cm

130 cm to 135 cm

135 cm to 140 cm

140 cm to 145 cm

145 cm to 150 cm

150 cm to 155 cm

This chart shows the heights of children in a year 6 class at school.

How many children are in the class? This chart shows the heights of children in a year 6 class at school.

Find the median class. 110 cm to 115 cm

115 cm to 120 cm

120 cm to 125 cm

125 cm to 130 cm

130 cm to 135 cm

135 cm to 140 cm

140 cm to 145 cm

145 cm to 150 cm

150 cm to 155 cm

This chart shows the heights of children in a year 6 class at school.

Estimate the total height of all the children in the class. This chart shows the heights of children in a year 6 class at school.

Estimate the mean height of all the children in the class to the nearest cm. This chart shows the heights of children in a year 6 class at school.

Find the modal class. 110 cm to 115 cm

115 cm to 120 cm

120 cm to 125 cm

125 cm to 130 cm

130 cm to 135 cm

135 cm to 140 cm

140 cm to 145 cm

145 cm to 150 cm

150 cm to 155 cm

This chart shows the heights of children in a year 6 class at school.

How many children are in the class? This chart shows the heights of children in a year 6 class at school.

Find the median class. 110 cm to 115 cm

115 cm to 120 cm

120 cm to 125 cm

125 cm to 130 cm

130 cm to 135 cm

135 cm to 140 cm

140 cm to 145 cm

145 cm to 150 cm

150 cm to 155 cm

This chart shows the heights of children in a year 6 class at school.

Estimate the total height of all the children in the class. This chart shows the heights of children in a year 6 class at school.

Estimate the mean height of all the children in the class to the nearest cm. • Question 1

This chart shows the heights of children in a year 6 class at school.

Find the modal class. 125 cm to 130 cm
• Question 2

This chart shows the heights of children in a year 6 class at school.

How many children are in the class? 24
EDDIE SAYS
1 + 3 + 7 + 5 + 4 + 3 + 1 = 24
• Question 3

This chart shows the heights of children in a year 6 class at school.

Find the median class. 130 cm to 135 cm
• Question 4

This chart shows the heights of children in a year 6 class at school.

Estimate the total height of all the children in the class. 3170
3170 cm
3170cm
EDDIE SAYS
(1 x 117.5) + (3 x 122.5) + (7 x 127.5) + (5 x 132.5) + (4 x 137.5) + (3 x 142.5) + (1 x 152.5) = 3170
• Question 5

This chart shows the heights of children in a year 6 class at school.

Estimate the mean height of all the children in the class to the nearest cm. 132
132 cm
132cm
EDDIE SAYS
3170 ÷ 24
• Question 6

This chart shows the heights of children in a year 6 class at school.

Find the modal class. 125 cm to 130 cm
• Question 7

This chart shows the heights of children in a year 6 class at school.

How many children are in the class? 25
EDDIE SAYS
2 + 6 + 5 + 4 + 3 + 2 + 3 = 25
• Question 8

This chart shows the heights of children in a year 6 class at school.

Find the median class. 130 cm to 135 cm
• Question 9

This chart shows the heights of children in a year 6 class at school.

Estimate the total height of all the children in the class. 3392.5
3392.5 cm
3392.5cm
EDDIE SAYS
(2 x 117.5) + (6 x 127.5) + (5 x 132.5) + (4 x 137.5) + (3 x 142.5) + (2 x 147.5) + (3 x 152.5) = 3392.5
• Question 10

This chart shows the heights of children in a year 6 class at school.

Estimate the mean height of all the children in the class to the nearest cm. 136
136 cm
136cm
EDDIE SAYS
3392.5 ÷ 25
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