In: Statistics and Probability
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.)
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