Question

What is the standard deviation of the following data set 1,1.2,4,1.28,4.1,5.3?

Answer 1

Memorize the definition of standard deviation: the sd is the square root of the average of the squared deviations of the mean. Wow. Let's do it.

Step 1. First we need the mean. That's easy. Add them up and divide by the count. Check if you get 16.88/5 = 2.81333.

Step 2. Now we're going to subtract this from each of the values, and square the result. Don't worry about negative signs, the squaring will get rid of those. Example for the first number:

(1 - 2.813)^2 = 3.29

The list of numbers I get is (rounded, in reality round as little as possible):

3.29, 2.60, 1.41, 2.35, 1.66, 6.18

Step 3: Add them all up. I get 17.49. 
Step 4: Divide by the count of numbers. 17.49/6 = 2.91
Step 5: Take the square root from this result. SQRT(2.91) = 1.707305

TIP: Use excel to do all these steps, then run the set of numbers through Excel's built-in sd function (called  STDEV.P) and see that you get the same result!