Question

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

16,20,13,5,13,11,7,15,6,11

Answer 1

Solution:

Given that,

16,20,13,5,13,11,7,15,6,11

a) The range =20 - 5 = 15

The mean of sample is   

x/n =  (16+20+13+5+13+11+7+15+6+11)

=11.7

The sample mean is 11.7

he population standard deviation is  

= n /(x - )²

⁼  9 (16 - 11.7 )²+ (20 - 11.7 )²+ (13 - 11.7 )²+ (5 -11.7 )² +( 13- 11.7 )²+ (11 - 11.7 )²+ (7 - 11.7 )²+ (15-11.7 )² +( 6 - 11.7 )²+( 11 - 11.7 )²

= 20.21

= 4.4955533585978

=4.50

The population standard deviation is 4.50

population variance= ( )²

⁼ (4.50 )²

population variance ^=20.25