Question

Calculate the standard deviation of three numbers 9,10,11

Answer 1

Step 1. Work out the mean

In the formula above μ (the greek letter "mu") is the mean of all our values ...

Example: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4

The mean is:

9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+420

= 14020 = 7

So:

μ = 7

 

Step 2. Then for each number: subtract the Mean and square the result

This is the part of the formula that says:



So what is xi ? They are the individual x values 9, 2, 5, 4, 12, 7, etc...

In other words x1 = 9, x2 = 2, x3 = 5, etc.

So it says "for each value, subtract the mean and square the result", like this

Example (continued):

(9 - 7)2 = (2)2 = 4

(2 - 7)2 = (-5)2 = 25

(5 - 7)2 = (-2)2 = 4

(4 - 7)2 = (-3)2 = 9

(12 - 7)2 = (5)2 = 25

(7 - 7)2 = (0)2 = 0

(8 - 7)2 = (1)2 = 1

... etc ...

And we get these results:

4, 25, 4, 9, 25, 0, 1, 16, 4, 16, 0, 9, 25, 4, 9, 9, 4, 1, 4, 9

 

Step 3. Then work out the mean of those squared differences.

To work out the mean, add up all the values then divide by how many.

First add up all the values from the previous step.

But how do we say "add them all up" in mathematics? We use "Sigma": Σ

Answer 2

Answer:

first find mean, then find |x-a| square  and then apply sd formula.

Step-by-step explanation: