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The mode of the given series is ____.

Marks
10-20
20-30
30-40
40-50
50-60
Frequency
12
35
45
25
13

see full answer

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Detailed Solution

The mode of the given series is 33.33.
Given data:

Marks	10-20	20-30	30-40	40-50	50-60
Frequency	12	35	45	25	13

Formula used:

M o d e = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

where,

l

= lower limit of modal class (the class with highest frequency),

h

=size of modal class interval,

f 1

= frequency of modal class,

f 0

= frequency of the class preceding modal class,

f 2

= frequency of the class succeeding the modal class.
Observing the table, we know that the modal class is “30-45” and its frequency is 45.
So,

l = 30

h = 10

f 1 = 45

f 0 = 35

f 2 = 25

Substitute the values in the formula

M o d e = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h M o d e = 30 + 45 − 35 2 × 45 − 35 − 25 × 10 M o d e = 30 + 1030 × 10 M o d e = 30 + 3.33 M o d e = 33.33

Thus, the value of mode for given series is 33.33.

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