Question

Consider the data set.

• 2,3,6,8,9

(a)

Find the range. (Enter an exact number.)

(b)

Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)

(c)

Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)

Answer 1

Solution:

Given that,

2,3,6,8,9

a) The range =9 -2 = 7

b )The mean of sample is   

x/n =  (2 + 3 + 6 + 8 + 9 / 5)

= 5.6

The sample mean is 5.6

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/4 (2 - 5.6 )²+ (3 - 5.6 )²+ (6 - 5.6)²+ (8- 5.6)² +( 9 - 5.6 )²

= 1/4 (10.24+1.44+0.04+0.64+14.44)

= 9.3

=3.04959

The sample standard deviation is 3.05

c) The population standard deviation is  

= n /(x - )²

⁼  5(x - )²

⁼  5 (2 - 5.6 )²+ (3 - 5.6 )²+ (6 - 5.6)²+ (8- 5.6)² +( 9 - 5.6 )²

= 7.44

=2.727636

The population standard deviation is 2.73