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The mean of the following distribution is 50. Find the value of a and the frequencies of 30 and 70

X 10 30 50 70 90

f 17 5a+3 32 7a-11 19

2
by REVIL

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X 10 30 50 70 90

f 17 5a+3 32 7a-11 19

by REVIL

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X F fx

10 17 170

30 5a+3 15a + 90

50 32 1600

70 7a-11 490 a - 77

90 19 1080

total 60 + 12a 505a + 2863

we have given mean = 50

∑fx/N = 50

505a + 2863/60 + 12a = 50

505a + 2863 = 50(60 +12a)

505a + 2863 = 3000+ 600a

505a + 600a = 3000- 2863

-5a = 137

a = -27.4

10 17 170

30 5a+3 15a + 90

50 32 1600

70 7a-11 490 a - 77

90 19 1080

total 60 + 12a 505a + 2863

we have given mean = 50

∑fx/N = 50

505a + 2863/60 + 12a = 50

505a + 2863 = 50(60 +12a)

505a + 2863 = 3000+ 600a

505a + 600a = 3000- 2863

-5a = 137

a = -27.4

f=17,5a,3,32,7a-11,19=68+12a-8

xi×fi=170+150a+90+1600+490a_770+1710=3480+640a-680

=2800+640a.

now,mean=2800+640a/68+12a-8

50=2800+640a/68+12a-8

now,doing cross multiplication.

50×(68+12a-8)=2800+640a

2800+640a=3400+600a-400

40a=200

a=200/40=5