15.10 Mean, Variance, & Standard Deviation

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Presentation transcript:

15.10 Mean, Variance, & Standard Deviation

Mean, Variance & Standard Deviation Mean = Average of the Data Add up and Divide by # of data points Denoted by Variance: (number-mean)2, add up, divide Standard Deviation is square root of Variance: denoted by “the sum of”

Normal Distribution Curve (Just look—don’t write)

Ex 1) The leading number of home runs in MLB for one season were: 43, 50, 52, 56, 70, 65, 50, 73, 57, 47, & 48 Find the Mean, Variance, & Standard Deviation 1) Mean: Add them up & Divide by 11:

Ex 1) The leading number of home runs in MLB for one season were: 43, 50, 52, 56, 70, 65, 50, 73, 57, 47, & 48 Find the Mean, Variance, & Standard Deviation 2) Variance: Find the difference between each value in the set of data and the mean Square them , Add them & Divide by # of data (n) x 43 50 52 56 70 65 73 57 47 48 Total –13 –6 –4 14 9 –6 17 1 –9 –8 169 36 16 196 81 36 289 1 81 64 969

Ex 1) The leading number of home runs in MLB for one season were: 43, 50, 52, 56, 70, 65, 50, 73, 57, 47, & 48 Find the Mean, Variance, & Standard Deviation 3) Standard Deviation: Take square root of Variance

T.O.O. Ex 2) Find the mean, variance, and standard deviation: 1, 4, 6, 6, 7, 8, 8, 8 x 1 4 6 7 8 Total –5 –2 1 2 2 2 25 4 1 4 4 4 42

Ex 3) What happens to the Mean, V, and SD when we add 2 to each number in previous problem? 1, 4, 6, 6, 7, 8, 8, 8  3, 6, 8, 8, 9, 10, 10, 10 x 3 6 8 9 10 Total –5 –2 1 2 2 2 25 4 1 4 4 4 42 Mean increases by 2 also! Var & SD stay same!

#9 WS Mean, Variance, & Standard Deviation CST QUIZ!!!!! Homework #9 WS Mean, Variance, & Standard Deviation CST QUIZ!!!!!