Displaying Distributions with Graphs

1. Displaying Distributions with Graphs 2.1a h.w: pg 105: 2, 5, 10, 11, 13 - 15 Target Goal: I can construct and interpret an ogive (relative cumulative frequency graph).

2. Relative frequency, cumulative frequency, percentiles, and ogives. • Percentile (pth percentile)- The value such that “p” percent of the observations fall at or below it. • Relative frequency - Divide count in each class by total number then multiply by 100 to convert to a percentage; “percent” . . . think: getting ready to do a pie chart. • Cumulative frequency - Add counts in frequency column that fall in or below current class interval.

3. Relative Cumulative Frequency Divide entries in cumulative frequency column by total number. Ogive pronounced [O-JIVE]. (presidents age) (Percents)(Ogive) (Counts) Relative Cum. Relative Class Frequency Freq. Freq. Cum. Freq. 40-44 2 2/44 = 4.5% 2 2/44 = 4.5% 45-49 7 7/44 = 15.9% 9 9/44 = 20.5% 50-54 13 55-59 12 60-64 7 65-69 3 Total 44

4. OGIVE: Relative cumulative frequency graph Graph of relative standing of an individual observation.

5. Various info you can find. • 60th % tile occurs at • age 55 is at about the Bill Clinton = 46 years: • About of all U.S. presidents were the same age as or younger than Bill Clinton or • Bill Clinton was younger than of all U.S. presidents when inaugurated.

6. How old was Obama when he was elected? Pg. 88

7. Pg. 88

8. Example: Drive Time Professor Moore, who lives a few miles outside a college town, records the time he takes to drive to the college each morning. Here are the times (in minutes) for 42 consecutive weekdays, with the dates in order along the rows:

9. d. Construct an Ogive for Professor Moore’s Drivetimes.Fill in first 2 rows of relative cum freq. table. We will fill in the rest of the graph together.Note: right most value in range corres. to relative cum. freq. % on ogive. Relative Cumulative Relative Drivetime Frequency FrequencyFrequencyCum.Freq. 6.5-6.91 2.4% 1 2.4% 7.0-7.42 4.8% 3 7.1% 7.5-7.98 19.0% 11 26.2% 8.0-8.411 26.2% 22 52.4% 8.5-9.012 28.6% 34 81.0% 9.1-9.46 14.3% 40 95.2% 9.5-9.91 2.4% 41 97.6% 10.0-10.41 2.4% 42 100%

10. Remember: begin ogive with a point at height 0% at left endpoint of lowest class interval; last point plotted should be at a point of 100% • 60th percentile occurs at about age 57

11. Graph Ogive (4 min)

12. 100 90 80 70 60 Relative Cumulative Frequency 50 40 30 20 10 0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 6.5 7.0 Drive Time (minutes)

13. Example: Drive Time cont. e. Use your ogive(graph) from b. to estimate the center and 90th percentile for the distribution. • center: about 8.4 How did you find the center? • From graph • Or 2ndSTAT:MATH:median • By hand: 42 observations, the average of the 21st and 22nd observation. (see table) • 90th percentile: approximately 9.4

14. f. Use your ogive to estimate the percentile corresponding to a drive time of 8.00 minutes. 8.0 is approximately the 26th percentile 100 90 80 70 60 Relative Cumulative Frequency 50 40 30 20 10 0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 7.0 Drive Time (minutes)

15. The End