**Question 1.Find variance and S.D. for the following set of numbers.7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6Solution:**

Given data:

7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6

The tabulated form of the above data is

Calculation of variance and S.D.

**Question 2.Find variance and S.D. for the following set of numbers.65, 77, 81, 98, 100, 80, 129Solution:**

**Question 3.Compute variance and standard deviation for the following data:Solution:**

**Question 4.Compute the variance and S.D.Solution:**

Calculation of variance of u:

**Question 5.Following data gives ages of 100 students in a college. Calculate variance and S.D.Solution:**

**Question 6.Find mean, variance and S.D. of the following data.Solution:**

Alternate Method:

Calculation of variance of u:

**Question 7.Find the variance and S.D. of the following frequency distribution which gives the distribution of 200 plants according to their height.Solution:**

Since data is not continuous, we have to make it continuous.

Calculation of variance of u:

**Question 8.The mean of 5 observations is 4.8 and the variance is 6.56. If three of the five observations are 1, 3, and 8, find the other two observations.Solution:**

= 4.8, Var (X) = 6.56, n = 5, = 1, = 3, = 8 ……(given)

Let the remaining two observations be x

_{4}and x

_{5}.

From (i), we get

= 5 or = 7

∴ The two numbers are 5 and 7.