Question

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 11, 9, 4, 6, 6. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) s = (b) Multiply each data value by 7 to obtain the new data set 77, 63, 28, 42, 42. Compute s. (Round your answer to one decimal place.) s =

Answer 1

Solution:

Given that,

11, 9, 4, 6 , 6

n = 5

a )The mean of sample is   

x/n =  (11 + 9 + 4 + 6 + 6 / 5)

= 7.2

The sample mean is 7.2

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/(5-1) (11 - 7.2 )²+ (9 - 7.2 )²+ (4 - 7.2 )²+ (6 - 7.2 )² +( 6 - 5.2 )²

= 1/4 (14.44+3.24+10.24+1.44+1.44)

= 30.8/4

= 7.7

= 2.8

The sample standard deviation is = s = 2.8

77, 63, 28, 42 , 42

n = 5

b )The mean of sample is   

x/n =  (77 + 63 + 28 + 42 + 42 / 5)

= 50.4

The sample mean is 50.4

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/(5-1) (77 - 50.4 )²+ (63 - 50.4 )²+ (28 - 50.4)²+ (42 - 50.4 )² +( 42 - 50.4 )²

= 1/4 (707.56+ 158.76+501.76+70.56+70.56)

= 1509.2/4

= 377.3

= 19.4

The sample standard deviation is = s = 19.4