Page 145 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes M D from M d
.
.
5. Coefficient of M.D. from M d
M
d
.
.
M D from M o
6. Coefficient of M.D. from M o
M
o
Example: Calculate mean deviation from mean and median for the following data of
heights (in inches) of 10 persons.
60, 62, 70, 69, 63, 65, 60, 68, 63, 64
Also calculate their respective coefficients.
Solution:

Calculation of M.D. from X

60 62 70 69 63 65 60 68 63 64
X 64.4 inches
10
Sum of observations greater than X = 70 + 69 + 65 + 68 = 272.

Sum of observations less than X = 60 + 62 + 63 + 60 + 63 + 64 = 372.
Also, k = 4 and k = 6
2 1
1
M.D. from X 272 372 ( 4 6)64. 4 = 2.88 inches
10
.
2 88
Also, coefficient of M.D. from X = 0.045
64 4
.
Calculation of M.D. from M
d
Arranging the observations in order of magnitude, we have
60, 60, 62, 63, 63, 64, 65, 68, 69, 70
63 64
The median of the above observations is = = 63.5 inches.
2
Sum of observations greater than M = 64 + 65 + 68 + 69 + 70 = 336
d
Sum of observations less than M = 60 + 60 + 62 + 63 + 63 = 308
d
Also, k = 5 and k = 5.
2 1
336 308 ( 5 5)63. 5
.
2 8
M.D. from M = = 2.8 inches
10
d
.
2 8
Also, the coefficient of M.D. from M = = 0.044.
.
d 63 5
Example: Calculate mean deviation from median and its coefficient from the given data:
X : 0 1 2 3 4 5 6 7 8 9
f : 15 45 91 162 110 95 82 26 13 2

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