Page 31 - Basic Statistics

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d. Standard Deviation

Standard deviation is the square root of the variance, ie the set of data on

population X1, X2 , …, XN, standard deviation of population can be calculated

with the following formula.

 X − X N 2
2
Standard deviation :  = i
N

For the sample data set X1, X2 , …, Xn standard deviation of sample can

be calculated by the following formula.

 X − X n 2
2
Standard deviation : S = i
n 1 -

Worked Example 2.5 :

For the following set of data sample : 4 7 8 9 22 26 29 37 40 48

Calculate :

a. Range

b. Interquartile range
c. Variance

d. Standard deviation

Worked solution :

a. Range : Rg = Xmax - Xmin = 48 – 4

= 44

~~* CHAPTER 2 NUMERICAL MEASURES TO SUMMARIZE DATA *~~