The Mean of the Folowing is 62.8 and the Sum of All the Frequencies is 50. Find the Missing Frequency F_1 and F_2 - Mathematics

The mean of the folowing is 62.8 and the sum of all the frequencies is 50. find the missing frequency f_1 and f_2

 Class 0-20 20-40 40-60 60-80 80-100 100-120 Freq 5 f_1 10 f_2 7 8

Solution

 class Freq (f) Mid value fx 0-20 5 10 50 20-40 f_1 30 30f_1 40-60 10 50 500 60-80 f_2 70 70f_2 80-100 7 90 630 100-120 8 110 880 total 30+f_1+f_2 2060+30f_1+70f_2

Now, ∑ f= 30+f_1+f_2 and ∑ fx=2060+30f_1+70f_2 .........(1)

∑ f=50; mean=62.8 ...........(2)

From(1)

30+f_1+f_2=50

f_1+f_2=20.........(3)

Using (1) and (2)

Mean=(2060+30f_1+70f_2)/50

62.8=(2060+30fi+70f_2)/50

2060+30f_1+70f_2=62.8xx50

2060+30f_1+70f_2=3140

30f_1+70f_2=1080

3f_1+7f_2=108........(4)

From (3)and (4)

f_1=8

f_2=12

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode)
Exercise 24 (B) | Q 9 | Page 362