Question

the mean of following distribution is xi 11,14,17,20 fi 3,6,8,7 . (A)15.6 (B)17 (C)14.8 (D)16.4​

Answer 1

We prepare the table as above.

Here, ∑f

i

=72+p+q.

But, ∑f

i

=100 (given).

∴ 72+p+q=100

p+q=28

Also, mean =

∑f

i

∑f

i

x

i

=

72+p+q

1160+15p+25q

=

72+(p+q)

1160+15(p+q)+10q

=

72+28

1160+15×28+10q

=

100

1580+10q

But mean = 16.6 (given)

∴

100

1580+10q

=16.6

1580+10q=1660

10q=80

q=8

p+q=28

p=28−q=28−8=20

Hence, p=20 and q=8