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1-7 Variance & Standard Deviation

1-7 Variance & Standard Deviation. Investigation…. Let’s take a look at the following two sets of notebook grades: A: {59, 60, 60, 62, 63, 64, 67, 68, 68, 69} B: {59, 63, 64, 64, 64, 64, 64, 64, 65, 69} Create a dotplot for each set of data…. 59 61 63 65 67 69.

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1-7 Variance & Standard Deviation

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  1. 1-7 1-7Variance &Standard Deviation

  2. 1-7 Investigation…. Let’s take a look at the following two sets of notebook grades: A: {59, 60, 60, 62, 63, 64, 67, 68, 68, 69} B: {59, 63, 64, 64, 64, 64, 64, 64, 65, 69} Create a dotplot for each set of data….

  3. 1-7 59 61 63 65 67 69 59 61 63 65 67 69 Set A Set B Mean: 64 64 Range: 10 10

  4. 1-7 Measures of Spread • Mean, Median, and sometimes mode are used as measures of the “center” of data • Deviation, Variance, and standard deviation are all measures of spread . These are used to measure how a set of data is distributed in relation to the mean.

  5. 1-7 Deviation • Deviation is the difference between each piece of data and the mean • A positive deviation means that the piece of data is greater than the mean • A negative deviation means that the piece of data is less than the mean

  6. 1-7 Variance • Variance is found by finding the sum of the squares of the deviations of each term • Then dividing by one less than the number of terms

  7. 1-7 Standard Deviation • Standard Deviation is found by finding the square root of the variance.

  8. 1-7 Example with a set of data • Let’s review the two sets of notebook grades: • A: {59, 60, 60, 62, 63, 64, 67, 68, 68, 69} • B: {59, 63, 64, 64, 64, 64, 64, 64, 65, 69} • Calculate the Standard Deviation for both sets of data…

  9. 1-7 Compare the results • Set A: Standard Deviation = 3.77 • Set B: Standard Deviation = 2.4

  10. 1-7 59 61 63 65 67 69 59 61 63 65 67 69 Revisit data sets: Set A Set B S.D. = 2.4 S.D. = 3.77

  11. 1-7 Population Var & S.D. • If data represents population and not a sample, you must use n instead of n-1 in variance formula

  12. 1-7 How to find SD in your calculator…

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