Question

Cumulative frequency table is given below. Which type of cumulative frequency is given? Try to build the frequencies of respective class intervals.

Runs	0-10	10-20	20-30	30-40	40-50
No of cricketers	3	8	19	25	30

Answer 1

Hint:
Here, we will first analyze the frequency table and state its type. As the data given to us is in continuous intervals, we will find the frequency of the intervals by subtracting previous values of the number of cricketers from the value of the number of cricketers in that particular interval.

Complete step by step solution:
We know that the cumulative frequency starting from lowest to highest is known as less type cumulative frequency distribution.
So, the cumulative frequency given to us is less than the cumulative frequency distribution as the cumulative frequency is starting from 3 and going up to 30.
Next, we have to build the frequencies of respective class interval
We know that cumulative frequency is calculated by adding each frequency in the table to the frequency above that row.
So, to find the frequency from the cumulative frequency we will subtract the value from the predecessor’s value in the table as follows,

Runs	No. of cricketers(Cumulative frequency)	Frequency
\[0 - 10\]	\[3\]	\[3\]
\[10 - 20\]	\[8\]	\[8 - 3 = 5\]
\[20 - 30\]	\[19\]	\[19 - 8 = 11\]
\[30 - 40\]	\[25\]	\[25 - 19 = 6\]
\[40 - 50\]	\[30\]	\[30 - 25 = 5\]

So we get our frequency table as

Frequency

\[3\]

\[5\]

\[11\]

\[6\]

\[5\]

Note:
Cumulative frequency is used to determine the number of observations that lies above the particular interval. We should always check that the sum of all the frequencies should be equal to the last value of cumulative frequency then our answer is correct. The distribution given to us is a continuous interval without any difference therefore we can easily find out the difference between the consecutive frequencies.