Question

Compute the value of mode for the following frequency distribution.
Class: Frequency:
100-110 4
110-120 6
120-130 20
130-140 32
140-150 33
150-160 8
160-170 2​

Answer 1

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Answer 2

Therefore the mode of the distribution is 140.38.

Step-by-step explanation:

Class             Frequency                  cf

100-110               4                              4

110-120                6                             10

120-130             20                             30

130-140             32                             62

140-150             33                             95 (Mode class)

150-160               8                             103

160-170                2                            105

Maximum frequency is 33 present in 140-150 class.

Then , mode class is 140-150.

L = lower limit of mode class = 140

f₀= The frequency of preceding class of mode class = 32

f₁= The frequency of mode class= 33

f₂= The frequency of succeeding class of mode class =8

c= The class length of mode class= (150-140)=10

Mode

$Z= L+\frac{f_1-f_0}{2f_1-f_0-f_2}$

    $=140+[\frac{33-32}{(2\times 33)-32-8} ].10$

    =140.3846

    ≈140.38

Therefore the mode of given distribution is 140.38.