Mean Deviation about Mean

Q. If the mean deviation of the numbers $1,1+d,1+2d,\dots ,1+100d$ from their mean is $255$, then $|d|$ is equal to

1. $20$
2. $10.1$
3. $20.2$
4. $10$

Q. If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is:

1. $51$
2. $30$
3. $50$
4. $31$

Q. The marks of some students were listed from total marks of $75.$ The standard deviation of marks was found to be $9.$ Subsequently, the marks were raised to a maximum of $100$ and variance of new marks was calculated. The new variance is

1. $81$
2. $122$
3. $144$
4. $196$

Q. The mean deviation about the mean for the following data :
$\begin{array}{cccccccc}{x}_i& 2& 3& 4& 5& 6& 7& 8\\ f_i& 5& 2& 3& 4& 5& 4& 2\end{array}$
is

1. $2.3$
2. $3.4$
3. $4$
4. $1.66$

Q. The mean deviation about the mean for the following data :
$5,6,7,8,6,9,13,12,15$ is :

1. $1.5$
2. $3.2$
3. $2.89$
4. $5$

Q.

If the mean deviation of the numbers $1,1+d,1+2d,\cdot ,1+100d$ from their mean is 255, then $d$ is equal to:

1. 20.0

2. 10.1

3. 20.2

4. 10.0

Q.

Number of goals scored by Ronaldo in champions league for past 10 years are as follows. {1, 3, 8, 4, 7, 6, 10, 12, 17, 10} Find the mean deviation about the mean.

1. 3

2. 3.6

3. 4

4. 3.4

Q. The variance of first $10$multiples of $3$ is

1. $64.25$
2. $54.25$
3. $70.25$
4. $74.25$