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Warm-Up

Warm-Up. Find the mean of the following calorie intake an individual has in one day. 1588, 3190, 2150, 2008, 1854, 1650, 2140. Notes 2.4 (Part 1). Measures of Variation. Range.

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Warm-Up

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  1. Warm-Up Find the mean of the following calorie intake an individual has in one day. 1588, 3190, 2150, 2008, 1854, 1650, 2140

  2. Notes 2.4 (Part 1) Measures of Variation

  3. Range • Range: is the difference from the maximum and minimum entry of a data set. It allows you to know how the data entries are dispersed. Ex 1 45 8 74 96 74 15 14 101 80 45 20 4 8

  4. Range • Range: is the difference from the maximum and minimum entry of a data set. It allows you to know how the data entries are dispersed. Ex 1 45 8 74 96 74 15 14 101 80 45 20 4 8 Range = 101 - 4 = 97

  5. Deviation Deviation: is the difference of a data entry to the mean of the data set. • 5 6 10 14 16 24 35 Mean = 114 = 14.25 8

  6. 5 6 10 14 16 24 35 Mean = µ = 14.25 µ = mu Values Deviations X x - µ 4 5 6 10 14 16 24 35

  7. 5 6 10 14 16 24 35 Mean = µ = 14.25 µ = mu Values Deviations X x - µ 4 -10.25 5 6 10 14 16 24 35

  8. 5 6 10 14 16 24 35 Mean = µ = 14.25 µ = mu Values Deviations X x - µ 4 -10.25 5 -9.25 6 -8.25 10 -4.25 14 -.25 16 1.75 24 9.75 35 20.75 ∑x=114 ∑ x - µ = 0

  9. 1) x - µ (deviations column) should always add up to zero 2) Deviation squared will always be positive since you are squaring the number Values Deviation Deviation Squared X x - µ (x - µ)² 4 -10.25 105.06 5 -9.25 6 -8.25 10 -4.25 14 -.25 16 1.75 24 9.75 35 20.75 ∑x=114 ∑ x - µ = 0

  10. 1) x - µ (deviations column) should always add up to zero 2) Deviation squared will always be positive since you are squaring the number Values Deviation Deviation Squared X x - µ (x - µ)² 4 -10.25 105.06 5 -9.25 85.56 6 -8.25 68.06 10 -4.25 18.06 14 -.25 0.06 16 1.75 3.06 24 9.75 95.06 35 20.75 430.56 ∑x=114 ∑ x - µ = 0 ∑ (x - µ)²= 805.48

  11. Warm-Up • 13 5 11 4 12 10 6 8 Find the values, deviation and deviations squared columns 1) Find the mean first 2) Values Deviation Deviation Squared X x - µ (x - µ)²

  12. Values Deviation Deviation Squared X x - µ (x - µ)² 1 13 5 11 4 12 10 6 8

  13. Mean = 70 = 7.7789 Values Deviation Deviation Squared X x - µ (x - µ)² 1 -6.778 45.941 13 5.222 27.269 5 -2.778 7.717 11 3.222 10.381 4 -3.778 14.273 12 4.222 17.825 10 2.222 4.937 6 -1.778 3.161 8 0.222 0.049 ∑ (x - µ)² = 131.553

  14. Notes 2.4 Part 2

  15. Sample Variance Sample variance = σ² = ∑ (x - µ)² n - 1

  16. Sample Standard Deviation Sample standard = σ = √∑ (x - µ)² deviation n - 1

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