FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.47Solution :
Table : Computation of Mean Deviation.
About Mean About Median
Serial No. () Dev. From A.M. Serial No. () Dev. From Med.
x ignoring ± signs x ignoring ± signs
| d | | d |
1 2 11 1 2 12
2 6 7 2 6 8
3 11 2 3 11 3
4 14 1 4 14 0
5 16 3 5 16 2
6 19 6 6 19 5
7 23 10 7 23 9
Total –– 40 Total –– 39
A.M. ( )
(^1) 2 6 11 14 16 19 23 (^19113)
= 7 + + + + + + = 7 × = Median = size of 7 1 2 + th iterm = size of 4th item = 14
Mean deviation (about mean) =^ n|d|=^407 =5.71 Mean deviation (about median) =^ n|d|=^397 =5.57
Note : The sum of deviation (∑|d|) about median is 39, less than | d | about mean (= 40). Also M.D.
about median.(i.e.5.57) is less than that about mean, (i.e., 5.71)
Coefficient of Mean Deviation :
About mean, Coefficient of M.D =MeanM.D. =5.71 13 = 0.44 (app.)
About median, Coefficient of M. D. =MedianM.D. =5.57 14 = 0.40 (app.)
(b) For Discrete Series (or Simple Frequency Distribution)
The formula for computing M.D. is
i i
i
f x x
M.D. f
−
=∑
∑ or
fx x f|d|
f f
−
∑ =∑
∑ ∑
Where | d | = deviations from mean (or median) ignoring ± signs.