Consider the following statements :

1. Variance is unaffected by change of origin and change of scale.
2. Coefficient of variance is independent of the unit of observations.

Which of the statements given above is/are correct ?

• 1only

• 2 only

• Both 1 and 2 

• Neither 1 nor 2

What is the mean deviation from the mean of thenumbers 10, 9, 21, 16, 24 ?

• 5.2

• 5.0

• 4.5

• 4.0

33.

If the total number of observations is 20, $⅀{\mathrm{x}}_{\mathrm{i}}$= 1000 and $⅀{\mathrm{x}}_{\mathrm{i}}$ = 84000, then what is the variance of the distribution ?

• 1500

• 1600

• 1700

• 1800

For the data 3, 5, 1, 6, 5, 9, 5, 2, 8, 6

the mean, median and mode are x, y and z respectively.Which one of the following is correct.

• $\mathrm{x} = \mathrm{y} \ne \mathrm{z}$

• $\mathrm{x} \ne \mathrm{y} = \mathrm{z}$

• $\mathrm{x} \ne \mathrm{y} \ne \mathrm{z}$

• x = y = z

Consider the following statements in respect of a histogram :

1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the x-axis.

2. When class intervals are unequal in a frequency distribution. the area of the rectangle is proportional to the frequency.

Which of the above statements is/are correct ?

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

Consider the following statements:

1. The mean and median are equal in symmetric distribution.

2. The range is the difference between the maximum value and the minimum value in the data.

3. The sum of the areas of the rectangles in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis. 

Which of the above statements are correct ?

• 1 and 2 only

• 2 and 3 only

• 1 and 3 only

• 1, 2 and 3

The scores of 15 students in an examination wererecorded as 10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change ?

• Mean and median 

• Median and mode

• Mode only

• Mean and mode

In a study of two groups, the following results were obtained :

	Group A	Group B
Sample size	20	25
Sample mean	22	23
Sample standard deviation	10	12

Which of the following statements is correct ?

• Group A is less variable than Group B because Group A's standard deviation is smaller

• Group A is less variable than Group B because Group A's sample size is smaller

• Group A is less variable than Group B because Group A's sample mean is smaller.

• Group A is less variable than Group B because Group A's coefficient of variation is smaller.

Consider the following statements in respect of class intervals of grouped frequency distribution : 

1. Class intervals need not be mutually exclusive.

2. Class intervals should be exhaustive.

3. Class intervals need not be of equal width.

Which of the above statements are correct ?

• 1 and 2 only

• 2 and 3 only

• 1 and 3 only

• 1, 2 and 3

Two variates, x and y, are uncorrelated and have standard deviations ${\mathrm{\sigma }}_{\mathrm{x}} \mathrm{and} {\mathrm{\sigma }}_{\mathrm{y}}$ respectively. What is the correlation coefficient between x + y and x - y ?

• $\frac{{\mathrm{\sigma }}_{\mathrm{x}}{\mathrm{\sigma }}_{\mathrm{y}}}{{{\mathrm{\sigma }}_{\mathrm{x}}}^2 + {{\mathrm{\sigma }}_{\mathrm{y}}}^2}$

• $\frac{{\mathrm{\sigma }}_{\mathrm{x}} + {\mathrm{\sigma }}_{\mathrm{y}}}{2{\mathrm{\sigma }}_{\mathrm{x}}{\mathrm{\sigma }}_{\mathrm{y}}}$

• $\frac{{{\mathrm{\sigma }}_{\mathrm{x}}}^2 - {{\mathrm{\sigma }}_{\mathrm{y}}}^2}{{\mathrm{\sigma x}}^2 + {{\mathrm{\sigma }}_{\mathrm{y}}}^2}$

• $\frac{{\mathrm{\sigma }}_{\mathrm{y}} - {\mathrm{\sigma }}_{\mathrm{x}}}{{\mathrm{\sigma }}_{\mathrm{x}}{\mathrm{\sigma }}_{\mathrm{y}}}$