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Shift and Scale Changes

Shift and Scale Changes. Module 4b. Distribution Properties. Shift Changes: adding or subtracting a number from the each of the values. mean. Distribution Properties. Shift Changes: adding or subtracting a number from the mean. Distribution Properties.

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Shift and Scale Changes

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  1. Shift and Scale Changes Module 4b

  2. Distribution Properties • Shift Changes: adding or subtracting a number from the each of the values. mean

  3. Distribution Properties • Shift Changes: adding or subtracting a number from the mean.

  4. Distribution Properties • Shift Changes: adding or subtracting a number from the mean.

  5. Distribution Properties • The mean, median, Q1, Q3, maximum, and minimum all shift when there is a shift change. The shift change, say c, is added or subtracted to each of the statistics accordingly. • The measures of spread (standard deviation, variance, IQR, and range) do not change when there is a shift change.

  6. Distribution Properties • Scale Changes: multiplying or dividing each of the values by a number. mean

  7. Distribution Properties • Scale Changes: multiplying or dividing each of the values by a number.

  8. Distribution Properties • Scale Changes: multiplying or dividing each of the values by a number.

  9. Distribution Properties • The mean, median, Q1, Q3, maximum, and minimum all change when there is a scale change unless they are zero. Each is multiplied or divided by the scale change c. • The measures of spread (standard deviation, variance, IQR, and range) always change when there is a scale change. The standard deviation, IQR, and range are multiplied or divided by the scale change c. The variance is multiplied or divided by c2.

  10. Distribution Properties • Suppose we measure the weight of everyone on a football team and obtain the following statistics for a team report: • Mean: 230 lbs. Median: 240 lbs. • Std. Dev.: 50 lbs. Q1: 200 lbs., Q3: 280 lbs. • Variance: 2500 lbs. IQR: 80 lbs • Min.: 170 lbs. Range: 180 lbs. • Max.: 350 lbs.

  11. Distribution Properties • Now suppose we find that the scale was 10 lbs. under, so we need to add 10 lbs. to every weight. What would happen to each of the following statistics? Original After Shift Change • Mean: 230 lbs. • Median: 240 lbs. • s: 50 lbs. • Q1: 200 lbs. • Q3: 280 lbs.

  12. Distribution Properties • Now suppose we found out the scale was 10 lbs. under so we need to add 10 lbs. to every weight. What would happen to each of the following statistics? Original After Shift Change • Variance: 2500 lbs. • IQR: 80 lbs. • Min: 170 lbs. • Max: 350 lbs. • Range: 180 lbs.

  13. Distribution Properties • Further, suppose we find that we are supposed to report the weights and statistics in kilograms, not lbs (Remember, 1 lb = 0.6 kilograms). What would happen to each of the following statistics? After Shift Change After Shift and Scale Change • Mean: 240 lbs. • Median: 250 lbs. • s: 50 lbs. • Q1: 210 lbs. • Q3: 290 lbs.

  14. Distribution Properties • Further, suppose we found out that we are supposed to report the weights and statistics in kilograms, not lbs (Remember, 1 lb = 0.6 kilograms). What would happen to each of the following statistics? After Shift Change After Shift and Scale Change • Variance: 2500 lbs. • IQR: 80 lbs. • Min: 180 lbs. • Max: 360 lbs. • Range: 180 lbs.

  15. Distribution Properties • Now our report is ready!

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