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 \[x_i\]	\[f_i x_i\]	\[\left| x_i - X \right|\] = \[\left| x_i - 49 \right|\]	\[f_i \left| x_i - X \right|\]
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
	\[N = \sum^8_{i = 1} f_i = 110\]		\[\sum^8_{i = 1} f_i x_i = 5390\]		\[\sum^8_{i = 1} f_i \left| x_i - X \right| = 1644\]

\[N = \sum^8_{i = 1} f_i = 110\]
and

\[\sum^8_{i = 1} f_i x_i = 5390\]

\[X = \frac{\sum^8_{i = 1} f_i x_i}{N}\]
\[ = \frac{5390}{110}\]
\[ = 49\]

\[\text{ Mean deviation } = \frac{\sum^8_{i = 1} f_i \left| x_i - X \right|}{N}\]

\[ = \frac{1644}{110}\]

\[ = 14 . 945\]

\[ \approx 14 . 95\]