Averages from Grouped Data

In this worksheet, students read grouped data from frequency tables 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 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

55 ≤ m < 60
EDDIE SAYS
The modal class is the one with the highest frequency.
• 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

50 ≤ m < 55
EDDIE SAYS
The total frequency here is 28 This means the median is the 14th value. Using the cumulative frequencies, the 14th value is in the class 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

1490
EDDIE SAYS
The total mass is sum of the midpoints multiplied by the frequency for each interval. (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

53
EDDIE SAYS
The total mass is given as the sum of the midpoints multiplied by the frequencies (1490) The total frequency is the sum of the frequencies (28) 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

50 ≤ m < 55
EDDIE SAYS
The modal class is the one with the highest frequency.
• 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

50 ≤ m < 55
EDDIE SAYS
The total frequency here is 24 This means the median is the 12th value. Using the cumulative frequencies, the 12th value is in the class 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

1295
EDDIE SAYS
The total mass is sum of the midpoints multiplied by the frequency for each interval. (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

54
EDDIE SAYS
The total mass is given as the sum of the midpoints multiplied by the frequencies (1295) The total frequency is the sum of the frequencies (24) 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

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

53
EDDIE SAYS
The total mass is given as the sum of the midpoints multiplied by the frequencies (1585) The total frequency is the sum of the frequencies (30) 1585 ÷ 30 = 52.8
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