Questions - Answers

1. Find the mean deviation about the median for the following continuous distribution.

2. Find the mean deviation about the mean for the distribution.

3. Find the Variance and Standard Deviation for the following frequency distribution.

4. Find the mean and variance using the step deviation method of the following tabular data giving the age distribution of 542 members.

5. The coefficient of variation of two distributions are 60 and 70 and their standard deviations are 21 and 16 respectively. Find their arithmetic means.

Sol: We use the formula

C.V. denotes the coefficient of variation,

σ denotes the standard deviation and

 denotes the arithmetic mean.

When C.V. = 60, σ  = 21, we have 60 = × 100
 = 35
 ∴  First Arithmetic Mean = 35
When C.V. = 70, σ  = 16, we have 70 = 

∴ Second Arithmetic Mean = 22.85

6. The mean of 5 observations is 4.4. Their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.

Sol: Let the two observations required be x and y.

⇒ 97 = x² + y² ............. (2)

⇒ (x + y)² = x² + y² + 2xy

(1) and (2) ⇒  36 = xy

Now, (x - y)² = (x + y)² - 4xy

                     = (13)² - 4(36)

                     = 25

∴ x - y = 5, x + y = 13

⇒ x = 9, y = 4

∴ The other two observations are 9 and 4.