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

x

22 ( )x x

n

“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:

43 50 52 56 70 65 50 73 57 47 48

11x

61156

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)56x

22 ( )x x

n

x 43 50 52 56 70 65 50 73 57 47 48 Total

x x2( )x x

–13 –6 –4 0 14 9 –6 17 1 –9 –8

169 36 16 0 196 81 36 289 1 81 64 969

969

11 88.1

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

2 88.1

88.1 9.4

T.O.O. Ex 2) Find the mean, variance, and standard deviation:

1, 4, 6, 6, 7, 8, 8, 8

1 4 6 6 7 8 8 8 486

8 8x

x 1 4 6 6 7 8 8 8 Total

x x2( )x x

–5 –2 0 0 1 2 2 2

25 4 0 0 1 4 4 4 42

22 ( )x x

n

42

5.38

5.3 2.3

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

8x

x 3 6 8 8 9 10 10 10 Tot

alx x

2( )x x

–5 –2 0 0 1 2 2 2

25 4 0 0 1 4 4 4 42

2 425.3

8

5.3 2.3

3, 6, 8, 8, 9, 10, 10, 10

648

8

Mean increases by 2 also!Var & SD stay same!

Homework

#9 WS Mean, Variance, & Standard Deviation

CST QUIZ!!!!!