Chapter 15 - Statistics

Example 4. The mean of the following frequency distribution is 62.8 and the sum of all frequency is 50. Complete the missing frequencies f1 and f2:

Class 0-20 20-40 40-60 60-80 80-100 100-120 Total
Frequency 5 f1 10 f2 7 8 50

Solution:-

Class f1 x1 f1x1
0-20 5 10 50
20-40 f1 30 30f1
40-60 10 50 500
60-80 f2 70 70f2
80-100 7 90 630
100-120 8 110 880
  50   2060+ 30f1 + 70f2

5 + f1 + 10 + f2 + 7 + 8 = 50

30 + f1 + f2 = 50

f1 + f2 = 20

f2 = 20 – f1 ----------- (i)

2060 + 30f1 + 70f2 = 3140

30f1 + 70f2 = 3140 – 2060

30f1 +70f2 = 1080

3f1 + 7f2 = 108 ---------------- (ii)

3f1 + 7(20 - f1) = 108

-4f1 + 140 = 108

-4f1 = 108 - 140

-4f1 = -32

f1 = 8

From (i) f2 = 20 – f1

                 = 20 – 8

                 = 12

 

Maths by Mr. M. P. Keshari
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Subjects Maths (Part-1) by Mr. M. P. Keshari
Chapter 9 Circle
Chapter 10 Tangents to a circle
Chapter 11 Geometrical Construction
Chapter 12 Troigonometry
Chapter 13 Height and Distance
Chapter 14 Mensuration
Chapter 15 Statistics
Chapter 16 Probability
Chapter 17 Co-ordinate Geometry