http://www.ck12.org Chapter 1. An Introduction to Analyzing Statistical Data
TABLE1.9:
Observed Data Deviations (x−x ̄^2 )
9. 5 − 1. 5 2. 25
11. 5 0. 5 0. 25
12 1 1
Sum of the squared
deviations= 3. 5Normally if you were finding a mean, you would now divide by the number of numbers(n). This is the part that
puzzles many beginning statistics students. Instead of dividing byn, we divide byn−1, which will be explained
later in this section. Dividing by 2 gives:
3. 5
2
= 1. 75
Remember that this number was obtained by squaring the deviations, so the result is much larger than it should
be. This quantity is actually called thevarianceand it will be very important in later chapters. The final step is to
“unsquare” the variance, or take the square root:
√
1. 75 ≈ 1. 32
This is the standard deviation! This means that in our sample, the “typical” value is approximately 1.32 units away
from the mean.
Technology Note: standard deviation on the TI-83 or 84
- Enter the above data in list[L1], as you did in the previous lesson (see first screen below).
- Then choose 1-Var Stats from the[CALC]submenu of the[STAT]menu (second screen).
- EnterL1 (third screen) and press[enter]to see the fourth screen.
- In the fourth screen, the symbolSxis the standard deviation.
Why n-1?
There are several ways to look at the need to divide the sum byn−1 when calculating the standard deviation. For
now, we will skip some of the more technical explanations that involve things like degrees of freedom that you will