7.6 Standard Deviation April 26, 2013

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:

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

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.

Finding the mean 𝑥 = 600+ 470+170+430+ 300 5 𝑥 =394 Mean (average)

Finding the Variance 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒= (600−394) 2 + (470−394) 2 + (170−394) 2 + (430−394) 2 + (300−394) 2 5 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒= 206 2 + 76 2 + (−224) 2 + 36 2 + (−94) 2 5 = 108,520 5 =21,704

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!

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