Question

the below given distribution gives the weights of 50 students in a class. find the mode of the data: weight ( in kg) 40_45 45_50 50_55 55_60 60_65 65_70 70_75 no of students is 4,6,10,18,7,3,2​

Answer 1

Mode of the data is 57.10

Step-by-step explanation:

Class :            40-45    45-50    50-55    55-60    60-65    65-70    70-75

Frequency :      4            6             10         18            7             3            2

Here n = 50

To find mode class :

Here is maximum frequency is 18,

∴ Mode class is 55-60.

L = Lower boundary of mode class =  55

f₁ = frequency of the mode class = 18

f₀ = frequency of the preceding class = 10

f₂ = frequency of the succeeding class = 7

c = class length of the mode class (60-55) = 5

$z=L+(\frac{f_1-f_0}{2\times f_1-f_0-f_2} )\times c$

$=55+(\frac{18-10}{2\times 18-10-7} )\times 5$

$=55+(\frac{8}{19} )\times 5$

= 55 + 2.1053

= 57.1053

≈ 57.10

Mode of the data is 57.10

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