Question

Consider the following sample.

12, 13, 8, 6, 6, 11

(a) Find the range.
  

(b) Find the variance. (Give your answer correct to two decimal places.)


(c) Find the standard deviation. (Give your answer correct to two decimal places.)

Answer 1

Solution :

Given, n = 6

12, 13, 8, 6, 6, 11

(a) Find the range,

The range of a data set in statistics is the difference between the largest and the smallest values

The range = 13 - 6

= 7

The range = 7

(c) Find the standard deviation s ,

=   

= (12 + 13.......+ 11)/6

= 9.33

Now ,

s =   

s = (12 - 9.33)² + ... + (11 - 9.33)² / 6 - 1

s = 3.08

The standard deviation s = 3.08

(b) Find the variance s²,

s² = 3.08² = 9.49

The variance s² = 9.49