Question

Mode of the following frequency distribution is 65 and the sum of
all the frequencies is 70. Find the missing frequencies x and y.
Class
0-20-40-
20 40 60
160-180-
80 100
100-120-
120 140
140-
160
Frequency 8
11
Х
12
у
9
9
5​

Answer 1

Answer:

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Answer 2

Concept:

Mean is the average value of a set of numbers

Median is  the middlemost value of a set of numbers.

Mode is the value with the highest frequency

mode=3median-2mode

mode= l+f₁-f₀)/(2f₁-f₀-f₂)xh

Given:

Mode of the following frequency distribution is 65 and the sum of

all the frequencies is 70.

Find:

The missing frequencies

Solution:

11+x+12+y+9++9+5=70

x+y=70-54

x+y=16

Mode=65

Modal class= 60-80

mode= l+f₁-f₀)/(2f₁-f₀-f₂)xh

[l = 60, h = 20, f₀ = x, f₁ = 12,f₂ = pm

65 = 60 + (12 - x)/(2(12) - x - y)x 20

65 - 60 = (12 - x)/(24 - (x + y))x20

5 = (12 - x)/(24 - 16) x 20

5 = (12 - x)/8 x 20            

5 * 2/5 = 12 - x

2 = 12 - x

x = 12 - 2 = 10

x + y = 16

10+ y = 16

y = 16 - 10 = 6

x = 10, y = 6

Therefore, the missing frequencies are 10 and 6

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