3.2 Measures of Variation Range: Standard Deviation: a measure that lets us know by how much a group of data differs Sample standard deviation s =
Σ(x − x )2
n −1
Sample Variance: same as sample standard deviation without the square root, if you already have sample standard deviation __________________________ Σ(x − x )2
2
Sample Variance s =
n −1
A green house was commissioned to develop an extra large rose for the Rose Bowl Parade. A random sample of blossoms yielded the following diameters (in inches) 2 3 4 5 6 8 10 10 Find the standard deviation x − x x (x − x )2 Population Statistics Σx
population mean µ=
N
σ=
Σ(x − µ )2
population standard deviation N
Notice the denominator is N, not n-­‐1 when doing population data. If you ever see SSx = Σ(x − µ )2 Coefficient of Variation: Lets you know what _____________________ the standard deviation is of the mean. s
σ
CV = ⋅100 = ⋅100 x
µ
Deals sells 8 different kinds of flashlights that cost 2.10 1.95 2.60 2.00 1.85 2.25 2.15 2.25 Find the coefficient of variation Chebyshev’s Theorem For ANY data set, and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least 1
1− 2 k
______________ of the data will fall within _________________________ ______________ of the data will fall within _________________________ _______________ of the data will fall within ___________________________