Find the range sample variance and sample standard deviation

Find the range, sample variance, and sample standard deviations for the given data.

20, 12, 24, 7, 28, and 11.

Range

R/4

s²

s

Solution

Here,

range = max - min = 28 - 7 = 21 [answer]

R/4 = 21/4 = 5.25 [answer]

Getting the mean, X,      
      
X =    17  
      
Setting up tables,      
x   x - X   (x - X)^2
20   3   9
12   -5   25
24   7   49
7   -10   100
28   11   121
11   -6   36
      
Thus, Sum(x - X)^2 =    340  
      
Thus, as       
      
s^2 = Sum(x - X)^2 / (n - 1)      
      
and n = 6 here,      
      
s^2 =    68 [ANSWER]
      
Thus,      
      
s = 8.246 [ANSWER]