Question

Find the sample variance and standard deviation. 7,53, 14, 50, 33, 26, 32, 30, 36, 32 Choose the correct answer below. Fill in the answer box to complete your choice. (Round to two decimal places as needed.) O A. 02 = O B. s² = Choose the correct answer below. Fill in the answer box to complete your choice. (Round to one decimal place as needed.) A. S= O B. G=

Answer 1

Here we have given that,

Xi
7
53
14
50
33
26
32
30
36
32
7
53
14
50
33
26
32
30
36
32

Now, we want to find the sample variance ($S^2$) and sample standard deviation (s)

n= Number of observation = 10

$S^2$= sample variance=
Σ(Xi - 32 η -1

To find $S^2$ first we need to find the sample mean $\bar x$   

$\bar x$= sample mean =$\frac{\sum xi}{n}$

=$\frac{7+53+ 14+50+33+26+32+30+36+32}{10}$

=31.3

Now,

$S^2$= sample variance=
Σ(Xi - 32 η -1

=

$\frac{(7-31.3)^2 +(53 -31.3)^2+ ... +(32-31.3)^2}{10-1}$

=196.23

i.e. here option B is correct $S^2$ = 196.23

s= sample standard deviation = $\sqrt{S^2}$

=$\sqrt{196.23}$

=14.01

i.e. here option A is correct s= 14.01

The $\sigma^2$ population variance and the $\sigma$ is the population standard deviation are the population parameters.