Question

Use the following data set to find the sample statistics for the following data set. 1. (N) or (n) 2. (x-bar) or (μ) 3. (σ) or (s) Thanks!

Answer 1

(1) N or n = 20

(2)
`\bar X \text{ or } \mu` = 43.4

(3) σ = 9.78 and s = 10.04.

Explanation:

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e.
`\bar X \text{ or } \mu` is given by;

Mean =
`(\sum X)/(n)`

=
`(51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42)/(20)`

=
`(868)/(20)` = 43.4

So, the value of
`\bar X \text{ or } \mu` is 43.4.

(3) The formula for calculating population standard deviation (
`\sigma`) is given by;

Standard deviation,
`\sigma` =
`\sqrt{(\sum (X - \bar X)^(2) )/(N) }`

=
`\sqrt{((51-43.4)^(2)+(48-43.4)^(2)+.......+(42-43.4)^(2) )/(20) }`

= 9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

Sample Standard deviation, s =
`\sqrt{(\sum (X - \bar X)^(2) )/(n-1) }`

=
`\sqrt{((51-43.4)^(2)+(48-43.4)^(2)+.......+(42-43.4)^(2) )/(20-1) }`

= 10.04