Question

Consider the data set. 2, 4, 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,

2,4,6,8,9

a) The range = 9 - 2 = 7

b )The mean of sample is   

x/n =  (2 + 4 + 6 + 8 + 9 / 5)

   = 29/ 5

= 5.8

The sample mean is 5.8

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/4 (2 - 5.8 )²+ (4 - 5.8 )²+ (6 - 5.8 )²+ (8 - 5.8 )² +( 9 - 5.8 )²

= 1/4 (14.44 + 3.24 + 0.04 + 4.84 + 10.24)

= 32.8/4

= 8.2

= 2.86

The sample standard deviation is = 2.86

c) The population standard deviation is  

= n /(x - )²

⁼  5 / (2 - 5.8 )²+ (4 - 5.8 )²+ (6 - 5.8 )²+ (8 - 5.8 )² +( 9 - 5.8 )²

= 5 / (14.44 + 3.24 + 0.04 + 4.84 + 10.24)

= 32.8/5

= 6.56

= 2.56

The population standard deviation is = 2.56