Mean Deviation from Mean for Discrete Series

Q.

If the arithmetic of the data given below is 28, find (a) the missing frequency and (b) the median of the series

$\begin{array}{ccccccc}\text{Profit per Retail shop (in Rs)}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of Retail shops}& 12& 18& 27& --& 17& 6\end{array}$

Q.

For the arithmetic progression, $a,(a+d),(a+2d),(a+3d),...,(a+2nd),$the mean deviation from the mean is

1. $\left(\frac{n(n+1)}{(2n–1)}\right)d$

2. $\left(\frac{n(n+1)}{(2n+1)}\right)d$

3. $\left(\frac{n(n–1)}{(2n+1)}\right)d$

4. $\frac{(n+1)d}{2}$

5. $\left(\frac{n(n–1)}{(2n–1)}\right)d$

Q.

If the arithmetic mean of the data given below is 28, find the missing frequency.

$\begin{array}{ccccccc}\text{Profit Per}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Retail Shop}& & & & & & \\ \text{Number of}& 12& 18& 27& -& 17& 6\\ \text{Retail Shops}& & & & & & \end{array}$

Q. Let $\overline{X}$ and M.D. be the mean and the mean deviation about $\overline{X}$ of n observations $x_i,i=1,2,.....,n.$ If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are :

1. $\overline{X},M.D.$
2. $\overline{X}+5m,M.D.+5$
3. $\overline{X},M.D.+5$
4. $\overline{X}+5,M.D.$

Q. Find the mean deviation about mean for the following data:

Score $\left(x\right)$	$6$	$20$	$8$	$18$	$16$	$12$	$14$	$10$
Frequency $\left(f\right)$	$2$	$7$	$11$	$27$	$18$	$13$	$17$	$5$