Question
Calculate mean standard deviation and mean deviation about mean from the following distribution :
|
Marks |
Students |
|
More than 20 |
50 |
|
More than 40 |
47 |
|
More than 80 |
41 |
|
More than 100 |
21 |
|
More than 120 |
9 |
Solution
Convert cumulative frequency with interval.
Calculation of Mean and Standard Deviation
|
Marks |
Frequency |
Mid-points |
m–90 d |
|
fd' |
fd'2 |
|
(x) |
(f) |
(m) |
d |
d' |
||
|
20 – 40 |
50 – 47 = 3 |
30 |
–60 |
–6 |
–18 |
108 |
|
40 – 80 |
47 – 41 =6 |
60 |
–30 |
–3 |
–18 |
54 |
|
80 – 100 |
41 – 21 = 20 |
90 |
0 |
0 |
0 |
0 |
|
100 – 120 |
21 – 9 = 12 |
110 |
+20 |
+2 |
24 |
48 |
|
120 – 140 |
9 – 0 = 9 |
130 |
+40 |
+4 |
36 |
144 |
|
N = 50 |
Σfd'=24 |
Σfd'2 = 354 |
Calculation of Mean Deviation from mean
|
Marks |
Frequency |
Mid-points |
m–94.8 |
f|D| |
|
X |
(f) |
(m) |
||
|
20 – 40 |
3 |
30 |
64.8 |
194.4 |
|
40 – 80 |
6 |
60 |
34.8 |
208.8 |
|
80 – 100 |
20 |
90 |
4.8 |
96 |
|
100 – 120 |
12 |
110 |
15.2 |
182.4 |
|
120 – 140 |
9 |
130 |
15.2 |
316.8 |
|
N = 50 |
Σf|D| = 998.4 |
