Question

. Marks obtained by 40 students in a short assessment is given below, where a and b are
two missing data.
Marks ============ 5 6 7 8 9
Number of Students= 6 A 16 13 b
If the mean of the distribution is 7.2, find a and b.

Answer 1

Sigma fi Xi fixi

6 5 6(5)=30

a 6 =6a

16 7 16(7)=112

13 8 13(8) =104

b 9 =9b

Summation of fixi=30+6a+112+104+9b=246+6a+9b

Summation of fi=6+a+16+13+b=40

=35+a+b=40

a+b=5.............(1)

Mean=sigmafixi/fi

7.2=246+6a+9b/40

288= 246+6a+9b

42=6a+9b............(2)

From (1) b=5-a sub in(2)

Then., 42=6a+9(5-a)

42=6a+45-9a

-3=-3a

a=-3/-3=1

Therefore, a=1............(3)

Sub (3) in (1)

a+b=5

1+b=5

b=5-1=4

Therefore., a=1 and b=4