State true or false.

The following is the distribution of weights (in kg) of $40$ persons.

The cumulative frequency table for the above data is-

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True

False

answer is A.

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Detailed Solution

Given a table of data.
Question Image

To construct the cumulative frequency distribution or less than type table for the data, further add the frequencies with the consecutive frequencies.
For the interval 40 – 45, the frequency is 4.
And so the cumulative frequency is 4.
For the interval 45 – 50, the frequency is 4.
And so the cumulative frequency is 4 + 4 = 8.
For the interval 50 – 55, the frequency is 13.
And so the cumulative frequency is 8 + 13 = 21.
For the interval 55 – 60, the frequency is 5.
And so the cumulative frequency is 21 + 5 = 26.
For the interval 60 – 65, the frequency is 6.
And so the cumulative frequency is 26 + 6 = 32.
For the interval 65 – 70, the frequency is 5.
And so the cumulative frequency is 32 + 5 = 37.
For the interval 70 – 75, the frequency is 2.
And so the cumulative frequency is 37 + 2 =39.
For the interval 75 – 80, the frequency is 1.
And so the cumulative frequency is 39 + 1 =40.
By forming the cumulative frequency, we get,
Question Image

The table is the same as the given table.
Hence, the given table is true.
Therefore, option 1 is correct.

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