Calculate the mode of the following frequency distribution

Seconds

51-55

56-60

61-65

66-70

Frequency

2

7

8

4

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Answer 1

Explanation:

Given,

The interval is not continuous, therefore subtract 0.5 from the lower limit and add 0.5 in the upper limit.

Now, the table will be

The interval with the highest frequency is 60.5 - 65.5.

Modal class = 60.5 – 65.5 ( Highest frequency = 8)

Formula

Mode = L + \(\big[\frac{f_1-f_0}{2f_1-f_0-f_2}\big]\) × I

I = class interval or class size = 5

f₁ = frequency of modal class = 8

f₀ = frequency of class preceding modal class = 7

f₂ = frequency of class succeeding modal class = 4

L = lower limit of modal class = 60.5

Mode = 60.5 + \(\big[\frac{8-7}{2\times 8-7-4}\big]\)× 5

= 60.5 + [\(\frac{1}{16-11}\)] × 5

= 60.5 + \(\frac{1}{5}\)× 5

= 60.5 + 1

∴ The mode is 61.5.

The correct answer is option (1).

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