The table given below shows the runs scored by a cricket team

Q) The table given below shows the runs scored by a cricket team during the overs of a match.

Estimate the modal runs scored.

ICSE Specimen Question Paper (SQP)2025

Ans: Since the modal class is the class with the highest frequency.

In the given question, class “50 – 650” has 60 frequency which is the highest frequency among all other classes.

Hence, modal class is “50 – 60”.

Now mode of the grouped data is calculated by:

Mode = L + $[\frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)}]$ x h

Here,

L = lower class limit of modal class = 50

$f_1$ = frequency of modal class = 60

$f_0$ = frequency of class proceeding to modal class = 40

$f_2$ = frequency of class succeeding to modal class = 51

h = class size = 60 – 50 = 10

Let’s put values in the formula and solve:

Mode = L + $[\frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)}]$ x h

= 50 + $[\frac{(60 - 40)}{(2 (60) - 40 - 51)}]$ x 10

= 50 + $(\frac{20}{29})$ x 10

= 50 + $\frac{200}{29}$ = 50 + 6.897 = 56.897

Therefore, the modal value is 56.897

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