Question

IF THE MEAN OF THE FOLLOWING DISTRIBUTION IS 2.6 , then find the value of k. variables (Xi) are 1,2,3,4,5 resoectively and frequency (Fi) are 4,5,k,1 and 2 respectively

Answer 1

Given

X=1,2,3,4,5
F=4,5,k,1,2

Mean =2.6

Mean =€fx/€f

2.6=(1x4+2x5+3xk+4x1+5x2)/4+5+k+1+2

2.6=(4+10+4+10+3k)/12+k

2.6=(28+3k)/12+k

2.6(12+k)=(28+3k)

31.2+2.6k=28+3k

31.2-28=3k-2.6k

3.2=0.4k

K=3.2/0.4

K=8


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Answer 2

Given:

Mean=2.6

To find:

The value of k

Solution:

The value of k is 8.

The given mean can be obtained by dividing the sum of the variables and their frequency's product by the sum of their frequencies.

So, mean=∑xi×fi/∑fi

The value of ∑xi×fi is as follows-

=1×4+2×5+3×k+4×1+5×2

=4+10+3k+4+10

=28+3k

∑fi=4+5+k+1+2=12+k

Mean=2.6

2.6=(28+3k)/(12+k)

2.6(12+k)=28+3k

31.2+2.6k=28+3k

3.2=0.4k

8=k

Therefore, the value of k is 8.