1. 2.1 Describing Location in a Distribution

2. Percentiles
The pth percentile of a distribution is the value with p percent of the observations less than it.

3. Percentiles
The following stem and leaf plot represents the scores in Mr. Pryor’s statistics class. Jenny scored an 86. How did she perform on this test relative to her classmates.

4. Percentiles Determine the Percentiles Norman who scored a 72
Katie who earned a 93
The two students who earned scores of 80

5. Percentiles
NOTE: Some people define the pth percentile of a distribution as the value with p percent of observations Less than or equal to, however we are sticking strictly to less than.

6. Percentiles
The stem plot below shows the number of wins for each of the 30 major league teams in
The Minnesota Twins (66 wins)
Washington Nationals (98 wins)
Rangers and Orioles (93 wins)

7. Frequency Tables
Frequency Table- Displays the counts (frequencies) of a category
Relative Frequency- Divide the counts from the frequency table by the total number of values and multiply by 100- to get a percent

8. Frequency tables
Cumulative Frequency Table- Add the counts in the frequency column for the current class and all classes with smaller values
Relative Cumulative Frequency- Divide the entries in the cumulative frequency column by the total number and multiply by 100 to convert to a percent

9. Age of US Presidents at inauguration
Make a
Relative Frequency
Cumulative Frequency
Relative Cumulative Frequency

10. Age of US Presidents at inauguration
Frequency
Relative Frequency
Cumulative Frequency
Relative Cumulative Frequency
40-44 2
45-49 7
50-54 13
55-59 12
60-64
65-69 3

11. Relative Cumulative Frequency
Frequency Table
Median
Frequency
Relative Frequency
Cumulative Frequency
Relative Cumulative Frequency
35 to <40 1
40 to <45 10
45 to <50 14
50 to <55 12
55 to <60 5
60 to <65 6
65 to <70 3

12. Cumulative frequency graph
Plot the point corresponding to the cumulative relative frequency in each class at the smallest value of the next class These are sometimes also known as ogives

13. Inauguration ages of US Presidents

14. Inauguration ages of US Presidents
Was Barack Obama, who was first inaugurated at the age of 47 unusually young?
Estimate and interpret the 65th percentile of the distribution

15. Percentiles and quartiles
Q1- roughly 25% of the data or the 25th percentile
Q2 roughly 50%
Q3 roughly 75% of the data or the 75th percentile

16. Check your understanding

17. Check your understanding

18. Check understanding

19. Check understanding

20. Standardizing
We can describe Jenny’s location in the distribution of her class’s scores by telling how many standard deviations above or below the mean.

21. Z-score
A score tells how many standard deviations a value is from the mean. Observations larger than the mean have positive z scores. Observations smaller than the mean will have negative z-scores

22. Z-scores
Use the information from Mr. Pryor’s statistics class to determine the z-scores for
Jenny, who scored 86
Kate, who scored 93
Norman, who scored 72

23. Z-scores

24. Check your understanding