Advanced Math Topics

1. Advanced Math Topics 3.7 Percentile Rank

2. Percentile rank is a useful way to compare a number to a set of data by looking at all values below that number. Percentile rank has three accepted definitions. Here are examples of the three. We will use the third way to calculate the percentile rank. 1) The percentile rank or percentile of a term in a distribution is found by adding the percentage of terms below it. 2) The percentile rank or percentile of a term in a distribution is found by adding the percentage of terms below it with the percentage of terms equal to the given term. 3) The percentile rank or percentile of a term in a distribution is found by adding the percentage of terms below it with ½ the percentage of terms equal to the given term. The third definition is a weighted average of the first two and also allows the median to conveniently be the 50th percentile.

3. The number of terms equal to x, including x. The number of terms below x. B + ½ E • 100 Percentile rank of X = N The number of total terms, including x.

4. 1) The test scores of Ron and Kris are shown in the data below. They both scored 80 but they are in different classes. Find the percentile rank of each student. Ron’s Class 64, 67, 73, 73, 73, 74, 77, 77, 78, 78, 79, 80, 80, 82, 91, 94, 100 Kris’s Class 43, 65, 68, 73, 75, 76, 76, 77, 79, 80, 80, 80, 80, 85, 86, 87, 88, 90, 92, 96 ½ (2) 11 + Ron’s percentile rank = • 100 = 70.59 17 Ron’s percentile rank is 70.59. ½ (4) 9 + Kris’s percentile rank = • 100 = 55 20 Kris’s percentile is 55. She is in the 55th percentile.

5. 2) One hundred candidates for an acting job took a test on dancing ability, poise, singing, and acting ability. Calculate Heather’s percentile for her score of 43. We assume that all scores in Heather’s interval are the class mark of 44.5 Thus, these scores are above Heather’s and hers is the only score of 43. ½ (1) 31 + Heather’s percentile rank = • 100 100 = 31.5 What if Heather scored a 44.5? We assume that all scores in Heather’s interval are the class mark of 44.5 Thus, all 18 of these scores are equal to Heather’s score. ½ (18) 31 + Heather’s percentile rank = • 100 100 = 40 What if Heather scored a 48? We assume that all scores in Heather’s interval are the class mark of 44.5 Thus, 17 of these 18 scores are less than Heather’s score, the other is her score. Her score is the only one equal to 48. ½ (1) 48 + Heather’s percentile rank = • 100 = 48.5 100

6. Things to note… P37 is a shorthand way to denote the 37th percentile. The lower quartile is P25 or Q1. Thus, 25% of the values are below the lower quartile. It is the median of the lower half of thedata. The upper quartile is P75 or Q3. Thus, 75% of the values are below the upper quartile. It is the median of the upper half of the data. The interquartile range = upper quartile – lower quartile

7. HW P. 150 #1-5, 9a-c Let’s do #9 together. Answers: BOB is wrong for A, and therefore also for C. a) 11.5 b) 18 c) 6.5 Sub tomorrow, there will be a short reading and assignment to complete in class. Chapter 3 Test next Tuesday