Formula
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1. Mean deviation of Mean δˉx=∑f⋅|x-ˉx|n
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2. Mean deviation of Mean δˉx=∑f⋅|x-M|n
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3. Mean deviation of Mode δˉx=∑f⋅|x-Z|n
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Examples
1. Calculate Mean deviation about median from the following grouped data
| X | Frequency |
| 10 | 3 |
| 11 | 12 |
| 12 | 18 |
| 13 | 12 |
| 14 | 3 |
Solution:x
(1) | f
(2) | cf
(3) | |x-M|=|x-12|
(4) | f⋅|x-M|
(5)=(2)×(4) |
| 10 | 3 | 3 3=0+3
(3)=Previous (3)+(2) | 2 |x-12|=|10-12|=2 | 6 6=3×2
(5)=(2)×(4) |
| 11 | 12 | 15 15=3+12
(3)=Previous (3)+(2) | 1 |x-12|=|11-12|=1 | 12 12=12×1
(5)=(2)×(4) |
| 12 | 18 | 33 33=15+18
(3)=Previous (3)+(2) | 0 |x-12|=|12-12|=0 | 0 0=18×0
(5)=(2)×(4) |
| 13 | 12 | 45 45=33+12
(3)=Previous (3)+(2) | 1 |x-12|=|13-12|=1 | 12 12=12×1
(5)=(2)×(4) |
| 14 | 3 | 48 48=45+3
(3)=Previous (3)+(2) | 2 |x-12|=|14-12|=2 | 6 6=3×2
(5)=(2)×(4) |
| --- | --- | --- | --- | --- |
| -- | n=48 | -- | -- | ∑f⋅|x-M|=36 |
Median :
M = value of
(n2)th observation
= value of
(482)th observation
= value of
24th observation
From the column of cumulative frequency
cf, we find that the
24th observation is
12.
Hence, the median of the data is
12.
Mean deviation of Median
δˉx=∑f⋅|x-M|nδˉx=3648δˉx=0.75 Coefficient of Mean deviation
=δˉxˉx=0.7512=0.0625
2. Calculate Mean deviation about median from the following grouped data
Solution:x
(1) | f
(2) | cf
(3) | |x-M|=|x-2|
(4) | f⋅|x-M|
(5)=(2)×(4) |
| 0 | 1 | 1 | 2 | 2 |
| 1 | 5 | 6 | 1 | 5 |
| 2 | 10 | 16 | 0 | 0 |
| 3 | 6 | 22 | 1 | 6 |
| 4 | 3 | 25 | 2 | 6 |
| --- | --- | --- | --- | --- |
| -- | n=25 | -- | -- | ∑f⋅|x-M|=19 |
Median :M = value of
(n+12)th observation
= value of
(262)th observation
= value of
13th observation
From the column of cumulative frequency
cf, we find that the
13th observation is
2.
Hence, the median of the data is
2.
Mean deviation of Median
δˉx=∑f⋅|x-M|nδˉx=1925δˉx=0.76Coefficient of Mean deviation
=δˉxˉx=0.762=0.38
This material is intended as a summary. Use your textbook for detail explanation.
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