|
Calculation of Mean Deviation – Individual
Observations
Mean Deviation or M.D. = å
|D|/N
Where |D| within parallel line read as MOD(X - mean)
is the absolute value of the deviation from mean after
ignoring signs.
 
(i) Compute the mean of series.
(ii) Calculate the deviation of item from mean ignoring
sign and denote these deviations by |D|.
(iii) Calculate the total of these deviations, i.e.
|D|.
(iv) Divide the total obtained in step (iii) by the
number of observations.
Calculation of Mean Deviation – Discrete
Series
Mean Deviation or M.D. = å
f|D|/N
Where, |D| within parallel line read as MOD(X - mean)
is the absolute value of the deviation from mean after
ignoring signs.
(i) Compute the mean of series.
(ii) Calculate deviation of the item from mean ignoring
sign and denote these deviations by |D|.
(iii) Multiply these deviations by the respective
frequencies and obtain the total å
f|D|.
(iv) Divide the total obtained in step (iii) by the
number of observations. This gives the value of mean
deviation.
Calculation of Mean Deviation – Continuous
Series
For calculating the mean deviation in continuous
series, the procedure remains the same as discussed
above. The only difference is that here we have to
obtain the mid-point of the various classes and take
deviations of these points from median. The formula
is the same, i.e.,
M.D. = å f|D|/N
Q. 10. Compute the mean deviation for the
following set of data.
| Marks
|
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
70-80 |
| No.
of students |
5 |
14 |
10 |
8 |
6 |
4 |
Solution.
| Marks |
Midpoint
(M) |
Frequency
(f) |
f X M |
|D| = M – mean
|
f X |D| |
|
20-30 |
25
|
5 |
125
|
21.7
|
108.5
|
|
30-40 |
35
|
14
|
490
|
11.7
|
163.8
|
|
40-50 |
45
|
10
|
450
|
1.7
|
17.0
|
|
50-60 |
55
|
8 |
440
|
8.3
|
66.4
|
|
60-70 |
65
|
6 |
390
|
18.3
|
109.8
|
|
70-80 |
75
|
4 |
300
|
28.3
|
113.2
|
| |
|
å
N = 47 |
å
fM = 2195 |
|
å
f|D| = 578.7 |
Mean = å fM/N = 2195/47
= 46.70
M.D. = å f|D|/N =
578.7/47 = 12.31
|
