The mode of the following frequency distribution is 55

Q) The mode of the following frequency distribution is 55. Find the missing frequencies ‘a’ and ‘b’.

Ans: Since we know that, the modal class is the class with the highest frequency.

In the given data, class “45 – 60” has the highest frequency of 15.

Hence, class “45 – 60” is the modal class.

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

$f_1$ = frequency of modal class

$f_0$ = frequency of class proceeding to modal class

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

h = class size,

Let’s put values, we get

$55 = 45 + [\frac{(15 - a)}{(30 - 10 - a)}]$ x 15

$10 = [\frac{(15 - a)}{(20 - a)}]$ x 15

10 (20-a) = (15 – a)15

5a = 25

a = 5

Next, we will take the total of all frequencies:

51 = 6 + 7 + a + 15 + 10 + b

a + b = 51 – 38 = 13

Since a = 5, hence, b = 8

Therefore, the values of a & b are 5 & 8 respectively.

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