Question

Consider a sample with data values of 11, 4, 20, 8 and 7. Compute to variance and standard deviation.

Answer 1

solution:

given data

11, 4, 20, 8 ,7.

n=5

The mean of sample is   

x/n =  (11+4+20+8+7 / 5)

   = 50/ 5

= 10

The sample mean is 10

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/5-1 (11 - 10 )²+ (4 -10 )²+ (20 - 10 )²+ (8- 10 )² +( 7 - 10 )²

= 1/4 (1+36+100+4+9)

= 150/4

= 37.5

= 6.12

The sample standard deviation is 3.7

variance  s² = 1/(n-1)(x - )²

⁼1/5-1 (11 - 10 )²+ (4 -10 )²+ (20 - 10 )²+ (8- 10 )² +( 7 - 10 )²

⁼1/4 (1+36+100+4+9)

=150/4

variance s² =37.5