2. Let’s start with an example  I divided the class into 2 teams, A and B. Coincidentally, the quiz average for team A is the same as team B, 81.5. So we expect a graph of their scores to be about the same, right? Not so!

3. Let’s look at the scores: Mean

4. Standard Deviation is a number that tells us…  How far from “typical” a certain piece of data is.  How spread out the data items are.

5. Calculating the Standard Deviation, σ (sigma) Example  You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

6. Step 1: Calculate the mean Mean = 600 + 470 + 170 + 430 + 300 5 Mean = 1970 = 394 5 So the average height is 394 mm

7. Step 2: Calculate each dog’s difference from the mean.

8. Step 3: Square each of those results. Step 4: average the result.  We call this average the variance (σ 2 ) σ 2 = 206 2 + 76 2 + (-224) 2 + 36 2 + (-94) 2 5 σ 2 = 108,520 = 21,704 5

9. Step 5: Find the square root of the variance σ 2 to get the standard deviation σ  So, the Variance = 21,704.  And the Standard Deviation is just the square root of Variance, so: Standard Deviation: σ = √21,704 = 147

10.  And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the mean.  So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.

11.  Rottweillers are tall dogs. And Dachsunds are…well, a bit short... but don't tell them!

12. Z-score 1.4 σ