If for a distribution ∑ (x −5)=3, ∑ (x −5)² = 43 and the total number of item is 18, find the mean and standard deviation.

Given: for a distribution ∑ (x −5)=3, ∑ (x −5)² = 43 and the total number of item is 18

To find: the mean and standard deviation.

As per given criteria,

Number of items, n=18

And given ∑(x-5)=3,

And also given, ∑(x −5)² = 43

But we know mean can be written as,

Here assumed mean is 5, so substituting the corresponding values in above equation, we get

And we know the standard deviation can be written as,

Substituting the corresponding values, we get

Hence σ=1.54

So the mean and standard deviation of given items is 5.17 and 1.54 respectively.