Find the mode of the following frequency distribution:

Q) Find the mode of the following frequency distribution:

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

In the given question, class “40 – 50” has 17 frequency which is the highest frequency among all other classes.

Hence, modal class is “40 – 50”.

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 = 40

$f_1$ = frequency of modal class = 17

$f_0$ = frequency of class proceeding to modal class = 12

$f_2$ = frequency of class succeeding to modal class = 4

h = class size = 50 – 40 = 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

= 40 + $[\frac{(17 - 12)}{(2 \times 17 - 12 - 4)}]$ x 10

= 40 + $(\frac{5}{18})$ x 10

= 40 + $\frac{50}{18}$ = 40 + 2 $\frac{14}{18}$ = 42 $\frac{7}{9}$

Hence, the mode value is 42 $\frac{7}{9}$

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