The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively

• 45, 5

• 11.25, 1.25

• 11.25, 2.5

• 12.5, 2.5

In eight throws of a die, 5 or 6 is considered a success.The mean and standard deviation of total number of successes is respectively given by : 

• $\frac{8}{3}, \frac{16}{9}$

• $\frac{8}{3}, \frac{4}{3}$

• $\frac{4}{3}, \frac{4}{3}$

• $\frac{4}{3}, \frac{16}{9}$

Let the correlation coefficient between X and Y be 0.6. Random variables Z and W are defined as Z = X + 5 and W = $\frac{\mathrm{Y}}{3}$. What is the correlation coefficient between Z and W ?

• 0.1

• 0.2

• 0.36

• 0.6

If all the natural numbers between 1 and 20 are multiplied by 3, then what is the variance of the resulting series ?

• 99.75

• 199.75

• 299.25

• 399.25

If the correlation coefficient between x and y is 0.6, covariance is 27 and variance of y is 25, then what is the variance of x ?

• $\frac{9}{5}$

• $\frac{81}{25}$

• 9

• 81

$$\begin{gathered} \mathrm{Let} \overline{\mathrm{x}} \mathrm{be} \mathrm{the} \mathrm{mean} \mathrm{of} {\mathrm{x}}_1, {\mathrm{x}}_2, {\mathrm{x}}_3, ..., {\mathrm{x}}_{\mathrm{n}}. \mathrm{If} {\mathrm{x}}_{\mathrm{i}} = \mathrm{a} + \mathrm{cy}, \mathrm{for} \mathrm{some} \mathrm{constants} \\ \mathrm{a} \mathrm{and} \mathrm{c}, \mathrm{then} \mathrm{what} \mathrm{will} \mathrm{be} \mathrm{the} \mathrm{meanof} {\mathrm{y}}_1, {\mathrm{y}}_2, {\mathrm{y}}_3, ..., {\mathrm{y}}_{\mathrm{n}} ? \end{gathered}$$

• a + c$\overline{\mathrm{x}}$

• $\mathrm{a} - \frac{1}{\mathrm{c}}\overline{\mathrm{x}}$

• $\frac{1}{\mathrm{c}}\overline{\mathrm{x}} - \mathrm{a}$

• $\frac{\overline{\mathrm{x}} - \mathrm{a}}{\mathrm{c}}$

Consider the following statements :

1. Mean is independent of change in scale and change in origin.
2. Variance is independent of change in scale but not in origin.Which of the above statements is/are correct ?

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

8.

Consider the following statements :

1. The sum of deviations from mean is always zero.
2. The sum of absolute deviations is minimum when taken around media.                                    Which of the above statements is/are correct?

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

What is the median of the numbers

4.6, 0, 9.3, - 4.8, 7.6, 2.3, 12.7, 3.5, 8.2, 6.1, 3.9, 5.2 ?

• 3.8

• 4.9

• 5.7

• 6.0

In a test in Mathematics, 20% of the students obtained "first class". If the data are represented by a Pie-Chart, what is the central angle corresponding to "first class" ?

• $20°$

• $36°$

• $72°$

• $144°$