1. 7.6 Standard Deviation
April 26, 2013

2. Mean Variance Definition: Symbol: Definition:
The sum of numbers divided by how many numbers there are in the set of data (n). Also known as the “average” 𝑥 read as “x bar”
Symbol:
Variance
Definition:
The average of the squared differences from the mean.
( 𝑥 1 − 𝑥 ) 2 +( 𝑥 2 − 𝑥 ) 2 +( 𝑥 3 − 𝑥 ) 2 +…( 𝑥 𝑛 − 𝑥 ) 2 𝑛
Formula:

3. Standard Deviation Definition:
is a measure of how spread out numbers are.
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
 (sigma)
Formula:
Symbol:

4. You and your friends just measured the heights of your dogs
You and your friends just measured the heights of your dogs. The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm. Find out the Mean, the Variance, and the Standard Deviation.

5. Finding the mean
𝑥 = 𝑥 =394
Mean (average)

6. Finding the Variance
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒= (600−394) 2 + (470−394) 2 + (170−394) 2 + (430−394) 2 + (300−394) 2 5
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒= (−224) (−94) 2 5
= 108,520 5 =21,704

7. Finding the Standard Deviation
𝜎= 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝜎= 21,704 =147
So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.
Rottweilers are tall dogs. And Dachshunds are a bit short ... but don't tell them!

8. Homework
WS 7.6 Skip #1
“Class trip to the Coca Cola factory. I hope there is no pop quiz!”