The Mean Deviation.pptx

The Mean Deviation

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 𝑿 𝟏 , 𝑿 𝟐 , 𝑿 𝟑 , … , 𝑿 𝒏 , denoted by M. D. is given by 𝒏 𝒊=𝟏 𝒊 𝑴. 𝑫. = 𝟏 𝒏 𝑿 − 𝑿 (ungrouped data) 𝒏 𝑴. 𝑫. = 𝟏 𝒏 𝒇 𝒊 𝑿 𝒊 − 𝑿 (grouped data) 𝒊=𝟏 Where 𝑿 is the mean of the VALUES. The two vertical bars 𝑿 𝒊 − 𝑿 are absolute value symbols. They indicate that one should calculate the difference 𝑿 𝒊 − 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

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