GCSE Maths Unit 1 - Frequency Distribution Tables

March 3, 2016

GCSE Maths: Frequency Distribution Tables and Cumulative Frequency

 

The modal class is the class interval with the highest frequency. To get the mean of a distribution, we multiply each value by its frequency; add these together and divide by the total of the frequencies.

 

Example

Find the mode and mean of the distribution summarised in the table below.

Value

5

15

25

35

45

55

65

Frequency

2

4

5

6

4

2

1


Mode = 35 (it has the highest frequency 6)

Mean =  Frequency Distribution Tables and Cumulative Frequency

 

A cumulative frequency distribution table is similar to a normal frequency table except that we continuously add our frequencies to give a frequency for that class or lower. Once the cumulative frequencies have been plotted, both the median and the quartiles (half-way between the median and the ends, i.e.  1/4 or 3/4 - way through the data) can be easily read from the graph.

Example

i) Convert the frequency distribution table below into a cumulative frequency distribution table and then plot the data as a cumulative frequency graph.

Length

24

28

32

36

40

Frequency

3

7

12

6

4

ii) Use this graph to determine the median and both the lower and the upper quartiles of this data.

 

Length

24

28

32

36

40

Frequency

3

7

12

6

4

Cumulative Frequency

3

10 (7+3)

22 (10+12)

28 (22+6)

32 (28+4)



GCSE Maths - Frequency Distribution Tables and Cumulative Frequency

Solutions
 

Total cumulative frequency = 32

 

Lower Quartile @ frequency of 1/4 of the total

1/4 x 32 = 8, which corresponds to a length of 28

Median @ frequency of 1/2 of the total

1/2 x 32 = 16, which corresponds to a length of 30

Upper Quartile @ frequency of 3/4 of the total

3/4 x 32 = 24, which corresponds to a length of 33

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