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# Percentile

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### Percentile

1. 1. ? or row on tom ip itati o f prec y a bilit he prob t What is the average life span of a D-cell battery? h at’s W Ho w aff ect ive is t he H1 N1 vac cin e ? Which age group watches the most TV in a week? 1
2. 2. Introduction to Statistics  Data ­ numbers collected in a particular context that are studied for a purpose Statistics ­ branch of mathematics that tries to make meaning of the            collected data. measure of central tendency an average of the set of data and tends to be located near the centre of the data • Mean  • Median • Mode *Range ­ 2
3. 3. Memory Test A light scratch shower work chicken program soccer baby water computer kitchen magazine gymnasium family garbage bowling bell ceiling sleep countertop 3
4. 4. 4
5. 5. Memory Test B sound watch curtain bench basketball thunderstorm street rooster dress machine garage library cafeteria brother star house shell alcohol grocery winter 5
6. 6. 6
7. 7. Percentiles Percent score ­ how well you would have done on the test if it were marked out of 100 Example: Marjoy writes a test and scores 48 out of possible 60  marks.  Express this mark as a rate of percent.  7
8. 8. Percentile Rank Comparing a Raw Score to All Other Scores Suppose 100 students have written the same test as Marjoy.  Suppose only 10 of these students score less than 48 out of 60.  How does Marjoy's mark compare with the marks of the other  students who have written the same test?  Assume that no other student has scored exactly 48 out of 60.  8
9. 9. Suppose, however, that of the 100 students who have written the same test  as Marjoy, 90 of them score lower than 48 out of 60.  How does Marjoy’s mark now compare with the marks of the other  students?  Assume no other student scores 48 out of 60.  9
10. 10. Percentile Rank  indicates the percent of all scores that fall below a particular score.  • The higher the percentile rank, the better the score compared to the other scores. • The lower the percentile rank, the poorer the score compared to the other scores. B = number of scores Below a given score E = number of scores Equal to the given score, including the given score.        *if there are no other scores equal to the given score, then E = 0.  n = total number of scores 10
11. 11. The following is a set of 32 marks achieved by students on an examination worth 100 marks. Determine the percentile ranking for a raw score of 72. 11
12. 12. Mac writes a college entrance examination and scores 1440 out of a possible 1800. Of the 875 students writing the college entrance examination, 25 other students have the same score as Mac and 680 students have lower scores than him. a) Find Mac's percentile rank. b)In order to be considered for a particular college  program, Mac needs a percentile rank of 75 or better.  Is Mac's score high enough for him to be considered  for the program? 12
13. 13. Special Percentile Notation You can also use the letter P and a subscript to denote a particular percentile 13
14. 14. A survey is conducted of a community of 2000 families.  The survey yields the following percentiles on family income. P25 = \$23,500       P50 = \$32,000 P75 = \$48,000       P90 = \$100,000 • Approximately what percentage of families in the community earn more  than \$100,000 a year?  • Approximately what percentage of families in the community earn less  than \$48,000 a year?  • Approximately how many families in the community earn less than  \$23,500 a year? 14
15. 15. P25 = \$23,500       P50 = \$32,000 P75 = \$48,000       P90 = \$100,000 15
16. 16. Complete:  Assignment 1 iz tom orrow for a qu Pre pare 16