Question

Using the following sample data; 6, 7, 11, 6, 11, 5, 15, 11, 5;

Compute the sample standard deviation using either the computing formula or the defining formula.

	A.	3.6
	B.	3.5
	C.	3.4
	D.	3.3

Answer 1

Solution:

Given that,

5,5,6,6,7,11,11,11,15

n = 9

The mean of sample is   

x/n =  (5 + 5 + 6 + 6 + 7 + 11 + 11 + 11 + 15 / 9)

   = 77 / 9

= 8.56

The sample mean is 8.56

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1 / 9 - 1 (5 - 8.56 )²+ (5 - 8.56 )²+ (6 - 8.56 )²+ (6 - 8.56 )² +( 7 - 8.56)² + ( 11 - 8.56 )² + ( 11 - 8.56 )² + ( 11 - 8.56 )² + ( 15 - 8.56 )²

= 1/8 (12.6736 + 12.6736 + 6.5536 + 6.5536 + 2.4336 + 5.9536 + 5.9536 + 5.9536 + 41.4736 )

= 100.2224 / 8

= 12.5278

= 3.5

The sample standard deviation is 3.5

correct option is = B.