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Unit–28: Measures of Dispersion: Standard Deviation

22 +1 1 notes
24 +3 9

26 +5 25
28 +7 49
30 +9 81

32 +11 121
Sx = 252 Sd = 572
2
N = 12

S x
Arithmetic mean (M) =
N
25 2
M = = 21
12
 d  S 2
Standard Deviation (σ) =   N  

Here Sd = 572
2
N = 12
Putting values in the formulae

572
σ =
12
= 47.66
σ = 6.9 (Approx.)
if we want to do this question using short–cut method, then the computation is as follows

S ' d 2  S ' d  2
Formula is σ = −  
N  N 
Let us assume that the assumed mean (A) of the given value is 20.

obtained Marks (x) Variation (d) from assumed mean (a) square of variation (d’ )
2
here assumed mean = 20
10 –10 100
12 –8 64

14 –6 36
16 –4 16
18 –2 4
20 0 0

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