Q.
Find the mean deviation about the mean for the following data.
Marks
obtained
10-
20
20-
30
30-
40
40-
50
50-
60
60-
70
70-
80
Number of
students
2
3
8
14
8
3
2
| Marks obtained | 10- 20 | 20- 30 | 30- 40 | 40- 50 | 50- 60 | 60- 70 | 70- 80 |
| Number of students | 2 | 3 | 8 | 14 | 8 | 3 | 2 |
Statistics
Solution:
We make the following table from the given data.
Marks
obtained
Number
of
students$f_i$
Mid
points $x_i$
$f_ix_i$
$|x_i -\bar{x}|$
$f_i|x_i- \bar{x}|$
10-20
2
15
30
30
60
20-30
3
25
75
20
60
30-40
8
35
280
10
80
40-50
14
45
630
0
0
50-60
8
55
440
10
80
60-70
3
65
195
20
60
70-80
2
75
150
30
60
40
1800
400
Here, $N = \sum\limits^{7}_{i = 1} f_{i} = 40$,
$\sum\limits^{7}_{i = 1} f_{i}x_{i} = 1800$,
$\sum\limits^{7}_{i = 1} f_{i}\left|x_{i}-\bar{x}\right| = 400$
Therefore $\bar{x} = \frac{1}{N} \sum\limits^{7}_{i = 1} f_{i}x_{i} =\frac{1800}{40}=45$
and M.D. $\left(\bar{x}\right) = \frac{1}{N}\sum\limits^{7}_{i = 1} f_{i}\left|x_{i}-\bar{x}\right|= \frac{1}{40}\times400=10$
| Marks obtained | Number of students$f_i$ | Mid points $x_i$ | $f_ix_i$ | $|x_i -\bar{x}|$ | $f_i|x_i- \bar{x}|$ |
|---|---|---|---|---|---|
| 10-20 | 2 | 15 | 30 | 30 | 60 |
| 20-30 | 3 | 25 | 75 | 20 | 60 |
| 30-40 | 8 | 35 | 280 | 10 | 80 |
| 40-50 | 14 | 45 | 630 | 0 | 0 |
| 50-60 | 8 | 55 | 440 | 10 | 80 |
| 60-70 | 3 | 65 | 195 | 20 | 60 |
| 70-80 | 2 | 75 | 150 | 30 | 60 |
| 40 | 1800 | 400 |