NTSE Stage 2 SAT 2019 Exam Question Paper

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Question : 60 of 100

Marks: +1, -0

Observe the following data

Class	0-20	20-40	40-60	60-80	80-100	Total
Frequency	17	$f_1$	32	$f_2$	19	120

If the above data has mean 50, then missing frequencies

f_1

and

f_2

are respectively

28 and 24
24 and 28
28 and 30
30 and 28

Solution:

Class	frequency	Mid-values $(x_1)$	$f_1x_1$
0-20	17	10	170
20-40	$f_1$	30	30 $f_1$
40-60	32	50	1600
60-80	$f_2$	70	70 $f_2$
80-100	19	90	1710
Total	120

Here,

17+19+32+f_1+f_2=120

⇒f_1+f_2=52

......(i)
∵ mean

{∑f_ix_i}/{∑f_i}

⇒{3480+30f_1+70f_2}/120=50

⇒3f_1+7f_2=252

.....(ii)
from (i) and (ii), we have:

3f_1+7f_2=252

3f_1+3f_2=156

-\;\;\;-\;\;\;\;\;-

–––––––––––––

⇒f_2=24

⇒f_1=52-f_2=52-24=28

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