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Standard Deviation and Z score

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.

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Standard Deviation and Z score

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  1. Standard Deviation and Z score Algebra I

  2. 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?

  3. 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.

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

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

  6. 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=

  7. 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

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

  9. 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

  10. 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

  11. 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

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

  13. 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

  14. Z score • Finding z score. 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

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