The mean deviation is defined as the average of the absolute deviations of values from the average or mean. It is calculated by taking the deviations without considering positive or negative signs. For a set of values X1, X2, X3, etc., the mean deviation is calculated by summing the absolute value of each value minus the mean, and dividing by n. In an example of grouped data, the mean deviation was calculated to be 6.12 for a data set where the mean was 55.08.

1. THE MEAN DEVIATION

2. THE MEAN DEVIATION OR THE AVERAGE DEVIATION
The mean deviation is defined as the average of the absolute deviations of the
values from an average (e. g. mean or median); the deviations are taken
without considering algebraic signs.
The mean deviation of a set of n values 𝑿𝟏, 𝑿𝟐, 𝑿𝟑, … , 𝑿𝒏, denoted by M. D. is
given by
𝒏 𝒊=𝟏 𝒊
𝑴. 𝑫. = 𝟏 𝒏 𝑿 − 𝑿 (ungrouped data)
𝒏
𝑴. 𝑫. = 𝟏 𝒏 𝒇𝒊 𝑿𝒊 − 𝑿 (grouped data)
𝒊=𝟏
Where 𝑿 is the mean of the VALUES. The two vertical bars 𝑿𝒊 − 𝑿 are absolute
value symbols. They indicate that one should calculate the difference 𝑿𝒊 − 𝑿,
ignoring minus signs in case the difference is negative.

3. Find the mean deviation from the mean for the values 2, 3, 6, 8 and 11.
Solution:
Here the mean 𝑿 = 2+3+6+11 = 6
5 𝑴. 𝑫. =
𝑿 − 𝑿
𝒏
=
𝟐 − 𝟔 + 𝟑 − 𝟔 + 𝟔 − 𝟔 + 𝟖 − 𝟔 + 𝟏𝟏 − 𝟔
𝟓
=
− 𝟒 + − 𝟑 + 𝟎 + 𝟐 + 𝟓
𝟓
=
𝟒 + 𝟑 + 𝟎 + 𝟐 + 𝟓
𝟓
𝟏𝟒
=
𝟓
= 𝟐. 𝟖.
Example

4. EXAMPLE (GROUPED DATA)
 Find mean deviation from mean to the following data.
Marks 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79
f 8 87 190 86 20

5. EXAMPLE - GROUPED DATA (SOLUTIONS)
Marks f X fX 𝑿 − 𝑿 f 𝑿 − 𝑿
30 – 39 8 34.5 276 20.58 164.64
40 – 49 87 44.5 3871.5 10.58 920.46
50 – 59 190 54.5 10355 0.58 110.2
60 – 69 86 64.5 5547 9.42 810.12
70 – 79 20 74.5 1490 19.42 388.4
Total 391 --- 21539.5 --- 2393.82
𝑿 =
𝒇𝑿
𝒇
=
𝟐𝟏𝟓𝟑𝟗. 𝟓
𝟑𝟗𝟏
= 𝟓𝟓. 𝟎𝟖
𝑴. 𝑫. 𝒇𝒓𝒐𝒎 𝒎𝒆𝒂𝒏 =
𝟐𝟑𝟗𝟑. 𝟖𝟐
𝟑𝟗𝟏
= 𝟔. 𝟏𝟐

6. THANK YOU