Standard Deviation and Z score Algebra I

Standard Deviation Definition – When looking at a set of data, the distance away from the mean. The center is considered the most ‘typical’. How far from ‘typical’ is the data?

Standard Deviation Some data is more dispersed than others. They have the same mean, but the data is spread out more (or less) than the mean.

Greek Symbols σ – “sigma” symbol for standard deviation. µ - “mu” symbol for mean also sometimes written as x. σ²- “sigma squared” symbol for variance.

Standard Deviation Finding standard deviation in the calculator. STAT EDIT enter data CALC 1-VarStats ENTER standard deviation is shown as σx mean is shown as x

Example Find the standard deviation, mean and variance of the following set of data. 95 92 85 100 86 90 85 81 σ = µ = σ²=

Example Find the standard deviation, mean and variance of the following set of data. 95 92 85 100 86 90 85 81 σ = 5.83 µ = 89.25 σ²= 33.99

Another example Find the standard deviation, mean and variance for the following set of data: 72 65 70 80 25 75 68

Another example Find the standard deviation, mean and variance for the following set of data: 72 65 70 80 25 75 68 σ = 16.94 µ = 65 σ²= 286.96

Z score Definition – How many standard deviations above or below the mean. This is given to you on your formula sheet. x – the value in the data set µ - mean σ – standard deviation

Z score Finding z score. Find the mean and standard deviation in the calculator. The circled number is the value in the data set to use. Just plug in the numbers and solve. 72 63 70 68 65 72 75

Z score Finding z score. 72 63 70 68 65 72 75 First, find the mean and standard deviation z = x - µ σ

Z score Finding z score. 72 63 70 68 65 72 75 X = 65 (the element given) µ = 69.29 σ = 3.92 Now substitute these values into the formula. z = x - µ σ

Z score Finding z score. 72 63 70 68 65 72 75 x = 65 µ = 69.29 72 63 70 68 65 72 75 x = 65 µ = 69.29 σ = 3.92 z = x - µ z = 65 – 69.29 = -1.09 σ 3.92