Descriptive Statistics - Numerical Measures

  1. Types of Variables & Descriptive Goals
  2. Descriptive Goals:
  3. one quantitative variable
  4. What patterns are there?
  5. shape
  6. center
  7. spread
  8. Are there "outliers"?
  9. Numerical Measures for Quantitative Variables
  10. numerical measures of CENTER/LOCATION
  11. sample mean
  12. How is it computed?
  13. by hand? [see page 38]
  14. by graphing calculator?
  15. using Minitab? [Statistics/basic/descriptive]
  16. Intuition: how is it located on a histogram? [See Fig 2.18 on p.40]
  17. Is it sensitive to outliers or resistant to outliers?
  18. EXAMPLE: sample from 2000 BayState Marathon dataset
  19. median
  20. How is it computed?
  21. by hand? [see page 38]
  • by graphing calculator?
  • using Minitab? [Statistics/basic/descriptive]
  1. Intuition: how is it located on a histogram? [See Fig 2.18 on p.40]
  1. Is it sensitive to outliers or resistant to outliers?
  2. EXAMPLE: sample from 2000 BayState Marathon dataset

  • [see pages 40-41] How do the values of sample mean & median compare for a histogram which is...
  • symmetric?
  • skewed to the right?
  • skewed to the left?
  • EXAMPLE: sample from 2000 BayState Marathon dataset
  1. numerical measures of SPREAD
  2. range
  3. How is it computed?
  4. by hand? [see page 41]
  5. by graphing calculator?
  6. using Minitab? [Statistics/basic/descriptive]
  7. Intuition: how is it determined from a histogram?
  8. Is it sensitive to outliers or resistant to outliers?
  9. EXAMPLE: sample from 2000 BayState Marathon dataset
  10. InterQuartileRange (IQR)
  11. How is it computed?
  12. by hand? [see pages 41-42]
  • by graphing calculator?
  • using Minitab? [Statistics/basic/descriptive]
  1. Intuition: how is it determined from a histogram?
  2. Is it sensitive to outliers or resistant to outliers?
  3. EXAMPLE: sample from 2000 BayState Marathon dataset

  • standard deviation
  • How is it computed?
  • by hand? [see page 48]
  • by graphing calculator?
  • look for something denoted by "s" or by "n1"
  • Do NOT use something denoted by "sn" or by "n". [cf. page 52]
  • using Minitab? [Statistics/basic/descriptive]
  1. Intuition: SORT OF an "average" distance of data from the sample mean; stay tuned for better interpretations
  2. Is it sensitive to outliers or resistant to outliers?
  3. EXAMPLE: sample from 2000 BayState Marathon dataset
  1. Boxplots[see pages 43-44]
  2. Boxplots are, basically, a graphical display of the 5-number summary.
  3. Boxplots may be drawn vertically (as in Fig 2.14 on p.34) or horizontally.
  4. Where is the bottom/left end of the box located?
  5. Where is the top/right end of the box located?
  6. Where is the box's line located?
  7. Boxplot rule for "outlier" status:any value whose distance to the box is more than 1.5IQR
  8. Where is the bottom/left "whisker" drawn?
  9. Where is the top/right "whisker" drawn?
  10. How are "outliers" portrayed?
  11. EXAMPLE: Discuss the thought question on page 34.
  12. Methods to obtain a boxplot:
  13. Be able to draw one by hand.
  14. Be able to get one from your graphing calculator. Many calculators offer two types:
  15. with no outlier identification
  16. with outlier identification
  17. using Minitab? [Graph/boxplot]
  18. EXAMPLE: sample from 2000 BayState Marathon dataset

  1. intro to ye olde Bell-Shaped Curve[section 2.7]
  2. This curve is one type of idealized model which turns out to fit many histograms rather well.
  3. Properties to know:
  4. It's a family of curves.
  5. All family members are bell-shaped (hence symmetrical).
  6. Where is the mean of a bell-shaped curve located?
  7. Where is the median of a bell-shaped curve located?
  8. Which values are "most likely"? Which are "least likely"?
  9. role of the standard deviation for a bell shaped curve
  10. What do the 3 parts of the Empirical Rule say? [see page 50 ff]
  • What is the resulting relationship between standard deviation and range? [p.51]
  • When will the Empirical Rule be accurate?
  • CD applet: See page 53 and run the applet from your CD.
  • EXAMPLE: sample from 2000 BayState Marathon dataset
  • z-scores
  • Be able to compute a z-score for any value relative to a given mean and standard deviation.
  • Interpretation:
  • for the sign of z:
  • for the magnitude of z: