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# Find the range, standard deviation, and variance for the following

### Resolved Question:

Find the range, standard deviation, and variance for the following sample data:
81, 84, 17, 53, 32, 74, 39, 85, 17, 3, 85, 84, 46, 71, 47, 7
Show all steps.
Submitted: 5 years ago.
Category: Math Homework
Expert:  David replied 5 years ago.

David :

hello

David :

the range is the difference between max and min values: 85-3=82

David :

the standard deviation is 29.91

Customer:

How did u get the standard deviation?

David :

you need to calculate the average first:

David :

51.5625

David :

then calculate the average of the squares for all these numbers

David :

it is 3497.1875

Customer:

I have to show all the steps to this problem

David :

OK give me 3-4 mins and I put all the steps in details, so it will be clear how the stdev is calculated

Customer:

ok

David :

here you go:

David :

there are in total 16 numbers the average of these numbers is: 51.5625
and the standrad deviation is defined s follows:
stdev = sqrt(1/15 * ((81-51.5625)+(84-51.5625)+(17-51.5625)
+(53-51.5625)^2+(32-51.5625)^2+(74-51.5625)^2+(39-51.5625)^2
+(85-51.5625)^2+(17-51.5625)^2+(3-51.5625)^2+(85-51.5625)^2
+(84-51.5625)^2+(46-51.5625)^2+(71-51.5625)^2+(47-51.5625)^2+(7-51.5625)^2) = 29.90645137

the variance is a square of this:

variance =(NNN) NNN-NNNN/strong>

David :

hope this helps

David :

let me know if this is clear.

Customer:

yes

David :

note that the average 51.5625 were calculated by adding all the numbers and dividing by 16.

Customer:

Thanks David!