 # Averages from Frequency Tables

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

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.

Example

This table shows the number of pets owned by children in a year 9 class at school.

Find the mean, median, mode and range.

Number of pets 0 1 2
Frequency 11 14 5

This means that:

11 children have no pets;

14 children have one pet;

5 children have two pets.

Mean

There are (11 x 0) + (14 x 1) + (5 x 2) = 0 + 14 + 10 = 24 pets in total.

There are 11 + 14 + 5 = 30 children in the class.

Mean number of pets = 24 ÷ 30 = 0.8

Median

There are 30 children, so the "middle person" will be the 15th and 16th.

The 15th and 16th person falls into the middle category and has 1 pet.

The median number of pets is 1

Mode

This is the one with the highest frequency.

Most children (14) have 1 pet.

The modal number of pets is 1

Range

The largest number of pets is 2 and the smallest is 0.

Range = 2 - 0 = 2

This table shows the number of pets owned by children in a year 9 class at school.

Find the mode.

Number of pets 0 1 2
Frequency 12 10 8
0

1

2

12

This table shows the number of pets owned by children in a year 9 class at school.

Find the range.

Number of pets 0 1 2
Frequency 12 10 8
0

1

2

4

This table shows the number of pets owned by children in a year 9 class at school.

Find the median.

Number of pets 0 1 2
Frequency 12 9 9
0

1

2

0.9

This table shows the number of pets owned by children in a year 9 class at school.

Find the mean.

Number of pets 0 1 2
Frequency 12 9 9
0

1

2

0.9

This table shows the number of pets owned by children in a year 9 class at school.

Find the mean.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0

0.625

1

1.5

This table shows the number of pets owned by children in a year 9 class at school.

Find the median.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0

0.625

1

1.5

This table shows the number of pets owned by children in a year 9 class at school.

Find the mode.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0

1

8

19

This table shows the number of pets owned by children in a year 9 class at school.

Find the range.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0

2

3

17

This table shows the number of pets owned by children in a year 9 class at school.

Find the range.

Number of pets 0 1 2 3 4
Frequency 8 10 12 2 0

0

2

3

4

This table shows the number of pets owned by children in a year 9 class at school.

Find the median.

Number of pets 0 1 2 3 4
Frequency 8 10 12 2 0

0

1

2

3

• Question 1

This table shows the number of pets owned by children in a year 9 class at school.

Find the mode.

Number of pets 0 1 2
Frequency 12 10 8
0
EDDIE SAYS
The mode is the column with the highest frequency.
• Question 2

This table shows the number of pets owned by children in a year 9 class at school.

Find the range.

Number of pets 0 1 2
Frequency 12 10 8
2
EDDIE SAYS
Remember when you are finding the range, we ignore the frequency column. Largest - Smallest 2 - 0 = 2
• Question 3

This table shows the number of pets owned by children in a year 9 class at school.

Find the median.

Number of pets 0 1 2
Frequency 12 9 9
1
EDDIE SAYS
The total frequency in this question is 30 We are looking for the 15th value. If we work through the frequencies, we see that the 15th value is in the 1 pet column
• Question 4

This table shows the number of pets owned by children in a year 9 class at school.

Find the mean.

Number of pets 0 1 2
Frequency 12 9 9
0.9
EDDIE SAYS
The mean is given by multiplying the frequency by the number of pets, adding all these answers and then dividing by the total frequency. Frequency x number of pets = (0 x 12) + (1 x 9) + (2 x 9) = 27 Total frequency is 30 Mean = 27 ÷ 30 = 0.9
• Question 5

This table shows the number of pets owned by children in a year 9 class at school.

Find the mean.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0.625
EDDIE SAYS
The mean is given by multiplying the frequency by the number of pets, adding all these answers and then dividing by the total frequency. Frequency x number of pets = (0 x 19) + (1 x 8) + (2 x 3) + (3 x 2) = 20 Total frequency is 32 Mean = 20 ÷ 32 = 0.625
• Question 6

This table shows the number of pets owned by children in a year 9 class at school.

Find the median.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0
EDDIE SAYS
The total frequency in this question is 32 We are looking for the 16th value. If we work through the frequencies, we see that the 16th value is in the 0 pet column.
• Question 7

This table shows the number of pets owned by children in a year 9 class at school.

Find the mode.

Number of pets 0 1 2 3
Frequency 19 8 3 2

0
EDDIE SAYS
The mode is the column with the highest frequency.
• Question 8

This table shows the number of pets owned by children in a year 9 class at school.

Find the range.

Number of pets 0 1 2 3
Frequency 19 8 3 2

3
EDDIE SAYS
Remember when you are finding the range, we ignore the frequency column. Largest - Smallest 3 - 0 = 3
• Question 9

This table shows the number of pets owned by children in a year 9 class at school.

Find the range.

Number of pets 0 1 2 3 4
Frequency 8 10 12 2 0

4
EDDIE SAYS
Remember when you are finding the range, we ignore the frequency column. Largest - Smallest 4 - 0 = 4
• Question 10

This table shows the number of pets owned by children in a year 9 class at school.

Find the median.

Number of pets 0 1 2 3 4
Frequency 8 10 12 2 0

1
EDDIE SAYS
The total frequency in this question is 32 We are looking for the 16th value. If we work through the frequencies, we see that the 16th value is in the 1 pet column
---- OR ----

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