Question

Compute mean deviation from mean of the following distribution:

Mark	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
No. of students	8	10	15	25	20	18	9	5

Answer 1

Computation of mean deviation from the mean:

Marks	Number of Students $f_i$	Midpoints $x_i$	$f_i{x}_i$	$\left|x_i-\overline{X}\right|$ =$\left|x_i-49\right|$	$f_i\left|x_i-\overline{X}\right|$
10−20	8	15	120	34	272
20−30	10	25	250	24	240
30−40	15	35	525	14	210
40−50	25	45	1125	4	100
50−60	20	55	1100	6	120
60−70	18	65	1170	16	288
70−80	9	75	675	26	234
80−90	5	85	425	36	180
	$N=\sum _{i=1}^8{f}_i=110$		$\sum _{i=1}^8{f}_i{x}_i=5390$		$\sum _{i=1}^8{f}_i\left|x_i-\overline{X}\right|=1644$

$N=\sum _{i=1}^8{f}_i=110$


and $\sum _{i=1}^8{f}_i{x}_i=5390$

$$\begin{gathered} \overline{X}=\frac{{\displaystyle \sum _{i=1}^8}{f}_i{x}_i}{N} \\ =\frac{5390}{110} \\ =49 \end{gathered}$$


$$\begin{gathered} \mathrm{Mean}\mathrm{deviation}=\frac{{\displaystyle \sum _{i=1}^8}{f}_i\left|x_i-\overline{X}\right|}{N} \\ =\frac{1644}{110} \\ =14.945 \\ \approx 14.95 \end{gathered}$$