Measure of Dispersion

Q. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is

1. 30
2. 30.1
3. 31
4. 29

Q. Let r be the range and $S^2=\frac{1}{n-1}{\sum }_{i=1}^n(x_i-\overline{x}{)}^2$, where S is the S.D. of a set of observations $x_1,x_2.....x_n$, then

1. None of these
2. 
3. 
4. 

Q. Let r be the range and $S^2=\frac{1}{n-1}{\sum }_{i=1}^n(x_i-\overline{x}{)}^2$, where S is the S.D. of a set of observations $x_1,x_2.....x_n$, then

1. $S\le r\sqrt{\frac{n}{n-1}}$
2. $S=r\sqrt{\frac{n}{n-1}}$
3. $S\ge r\sqrt{\frac{n}{n-1}}$
4. None of these

Q. What is the mean deviation about the mean for the following continuous frequency distribution?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 2-4& 5\\ 4-6& 6\\ 6-8& 3\\ 8-10& 1\end{array}$$

1. 2.12
2. 4.77
3. 1.33
4. 4.53

Q. The marks obtained by 10 students are 43, 48, 55, 57, 42, 50, 47, 48, 58, 50 then what is the standard deviation

Q. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is

1. 30
2. 30.1
3. 29
4. 31