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    CUMULATIVE FREQUENCY ANALYSIS


    In a data set, the cumulative frequency for a value ‘x’ is the total number of scores that are equal to or less than ‘x’.

    For example if we want to know the cumulative frequency regarding the scores of students in a class and assignment. The cumulative frequency suggests that thirty students received a test score of at most sixty, sixty students received a test score of at most sixty and hundred students received a test score of at most seventy.


    CUMULATIVE FREQUENCY TABLE

    Example

    A set of data given below shows the ages of participants in camp or in a summer camp. Draw a cumulative frequency table for the data.

    Age (years)

    Frequency

    Ten

    Seven

    Eleven

    Twelve

    Twelve

    Twenty seven

    Thirteen

    Ten

    Fourteen

    Twenty

    Solution – The cumulative frequency of the given data can be found by adding the current frequency with the previous frequency.

    The cumulative frequency of the first data will be same as the frequency because there is no cumulative frequency before it.

    Age (years)

    Frequency

    Cumulative Frequency

    Ten

    Seven

    Seven

    Eleven

    Twelve

    Seven + twelve = Nineteen

    Twelve

    Twenty seven

    Nineteen + twenty seven = Forty six

    Thirteen

    Ten

    Forty six + ten = fifty six

    Fourteen

    Twenty

    Fifty six + twenty = seventy six


    CALCULATION OF QUARTILES FROM CUMULATIVE FREQUENCY

    Quartile – The word quartile has been taken from the word quarter which means one fourth of something. Thus we can say that quartile means a certain fourth of a data set. When a certain set of data is arranged from the lowest to the highest, then it can be divided into four parts or quartiles.

    First quartile – This refers to the data set arranged from the lowest to the highest in one fourth parts i.e. (1 /4) parts.

    Second quartile – This refers to the data set arranged from the lowest to the highest in the second fourth parts i.e. (2 / 4) parts.

    Third quartile – This refers to the data set arranged from the lowest to the highest in the third fourth parts i.e. (3 /4) parts.

    Calculating quartiles from cumulative frequency

    Example – Calculate the first, second and third quartiles of the data set using the cumulative frequency curve.

    Age (years)

    Frequency

    ten

    six

    eleven

    ten

    twelve

    eighteen

    thirteen

    twenty

    fourteen

    nine

    fifteen

    five

    Solution -

    Age (years)

    Frequency

    Cumulative frequency

    ten

    six

    six

    eleven

    ten

    six + ten = sixteen

    twelve

    eighteen

    sixteen + eighteen = thirty four

    thirteen

    twenty

    thirty four + twenty = fifty four

    fourteen

    nine

    fifty four + nine = sixty three

    fifteen

    five

    sixty three + five = sixty eight

    sixteen

    two

    sixty eight + two = seventy

    Calculating quartiles –

    The cumulative frequency for the last element in the data set is seventy.

    Quartile one position = (seventy + one) / four = 17.75

    Quartile second position = 2(seventy + one) / four = 35.5

    Quartile third position = 3(seventy + one) / four = 53.25

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