Standard deviation help?

For my statistics homework, I have to calculate the standard deviation of a set of data:

1,8,2,4,3,5,15,9,3,10,3,12

I calculated 20.73 using the formula my prof gave us. But that doesn’t seem right, it’s way bigger than any of the numbers in that data set! I found standard deviation calculators online but they all give me answers ranging from 3-19, they all seem to use a different formula.

Can someone help me please?
Here is the equation my prof gave us to use, does it make any sense at all?
(I don’t have a sigma key or anything so I’ll just try to summarize it)

total of all data squared – (total of all data squared divided by number of total data)

divide that by the number of total data

find the square root

I get 20.73?

Mean = 6.25
Variances: -5.25, 1.75, -4.25, -2.25, -3.25, -1.25, 8.75, 2.75, -3.25, 3.75, -3.25, 5.75

Standard deviation is the square root of
the sum of the squares of the variances
divided by the (number of items – 1)

Standard Deviation = √[(-5.25² + 1.75² + -4.25² + -2.25² + -3.25² + -1.25² + 8.75² + 2.75² + -3.25² + 3.75² + -3.25² + 5.75²)/11] = 4.45

Edit:
Answer #3 lost me. And I’m staring at your prof’s explanation and it just doesn’t seem right. This is the method I’ve always used, but I was never good at statistics.

I’ll just offer one more thing, Σ is alt-228. The list of math alt-codes I use is http://www.usefulshortcuts.com/alt-codes/maths-alt-codes.php . There are many more out there, and some that are more complete, but I like this one.

Statistics – Standard Deviation song

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