The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the new set of values ?

• 10

• 20

• 40

• 70

12.

The standard deviation a of the first N natural numbers can be obtained using which one of the following formulae ?

• $\mathrm{\sigma } = \frac{{\mathrm{N}}^2 - 1}{12}$

• $\mathrm{\sigma } = \sqrt{\frac{{\mathrm{N}}^2 - 1}{12}}$

• $\mathrm{\sigma } = \sqrt{\frac{\mathrm{N} - 1}{12}}$

• $\mathrm{\sigma } = \sqrt{\frac{{\mathrm{N}}^2 - 1}{6\mathrm{N}}}$

The correlation coefficient computed from a set of 30 observations is 0.8. Then the percentage of variation not explained by linear regression is

• 80%

• 20%

• 64%

• 36%

Consider the following statements :

1. If 10 is added to each entry on a list, then the average increases by 10.
2. If 10 is added to each entry on a list, then the standard deviation increases by 10.
3. If each entry on a list is doubled, then the average doubles. Which of the above statements are correct ?

• 1, 2 and 3

• 1 and 2 only

• 1 and 3 only

• 2 and 3 only

The variance of 25 observations is 4. If 2 is added to each observation, then the new variance of the resulting observations is

• 2

• 4

• 6

• 8

The set of bivariate observations (x₁, y₁), (x₂, y₂ ), ... (x_n, y_n) are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then the possible values of the correlation coefficient between x and y are

• 0 and 1 only

• 0 and - 1 only

• 0, 1 and - 1

• - 1 and 1 only

An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry gives the following result :

	Firm A	Firm B
Number of workers	500	600
Average monthly wage	Rs. 1860	Rs. 1750
Variance of distributon of wages	81	100

The average of monthly wages and variance of distribution of wages of all the workers in the firms A and B taken together are

• Rs. 1860, 100

• Rs. 1750, 100

• Rs. 1800, 81

• None of the above

In any discrete series (when all values are not same) if x represents mean deviation about mean and y represents standard deviation, then which one of the following is correct ?

• $\mathrm{y} \ge \mathrm{x}$

• $\mathrm{y} \le \mathrm{x}$

• x = y

• $\mathrm{x} < \mathrm{y}$

The variance of 20 observations is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observations ?

• 5

• 10

• 15

• 45

The mean of a group of 100 observations was found to be 20. Later it was found that four observations were incorrect, which were recorded as 21, 21, 18 and 20. What is the mean if the incorrect observations are omitted ?

• 18

• 20

• 21

• 22