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Chapter 2: Describing Location In a Distribution

Chapter 2: Describing Location In a Distribution. Section 2.1 Measures of Relative Standing And Density Curves. Case Study. Read page 113 in your textbook. Where are we headed?. Last Chapter. Analyzed a set of observations graphically and numerically. This Chapter.

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Chapter 2: Describing Location In a Distribution

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  1. Chapter 2: Describing LocationIn a Distribution Section 2.1 Measures of Relative Standing And Density Curves

  2. Case Study • Read page 113 in your textbook

  3. Where are we headed? Last Chapter Analyzed a set of observations graphically and numerically This Chapter Consider individual observations

  4. Consider this data set: 6 7 7 2334 7 5777899 8 00123334 8 569 9 03 How good is this score relative to the others?

  5. Measuring Relative Standing: z-scores • Standardizing: converting scores from the original values to standard deviation units

  6. Measuring Relative Standing:z-scores A z-score tells us how many standard deviations away from the mean the original observation falls, and in which direction.

  7. Practice: Let’s Do p. 118 #1

  8. Measuring Relative Standing:Percentiles • Norman got a 72 on the test. Only 2 of the 25 test scores in the class are at or below his. • His percentile is 2/25 = 0.08, or 8%. So he scores in the 8th percentile. 6 7 7 2334 7 5777899 8 00123334 8 569 9 03

  9. Mathematical Model For the Distribution Density Curves Histogram of the scores of all 947 seventh-grade students in Gary, Indiana. • The histogram is: • Symmetric • Both tails fall off smoothly from a single center peak • There are no large gaps • There are no obvious outliers

  10. Density Curves

  11. Density Curves: Normal Curve This curve is an example of a NORMAL CURVE. More to come later….

  12. Describing Density Curves • Our measure of center and spread apply to density curves as well as to actual sets of observations.

  13. Proportions in a Density Curve

  14. Describing Density Curves • MEDIAN OF A DENSITY CURVE: • The “equal-areas point” • The point with half the area under the curve to its left and the remaining half of the area to its right

  15. Describing Density Curves • MEAN OF A DENSITY CURVE: • The “balance point” • The point at which the curve would balance if made of solid material

  16. Mean of a Density Curve

  17. Usually Notation • Use English letters for statistics • Measures on a data set • x = mean • s = standard deviation • Use Greek letters for parameters • Measures on an idealized distribution • µ = mean • σ = standard deviation

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