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**Standard Deviation and Z score**

Algebra I

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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?

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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.

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

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**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

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Example Find the standard deviation, mean and variance of the following set of data. σ = µ = σ²=

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Example Find the standard deviation, mean and variance of the following set of data. σ = 5.83 µ = 89.25 σ²= 33.99

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Another example Find the standard deviation, mean and variance for the following set of data:

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Another example Find the standard deviation, mean and variance for the following set of data: σ = 16.94 µ = 65 σ²=

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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

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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.

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Z score Finding z score. First, find the mean and standard deviation z = x - µ σ

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

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**Z score Finding z score. 72 63 70 68 65 72 75 x = 65 µ = 69.29**

x = 65 µ = 69.29 σ = 3.92 z = x - µ z = 65 – = -1.09 σ

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