Describing Location in a Distribution The pth percentile is the value with p percent of the observations LESS than it. (Alternate wording: p percent of.

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Presentation transcript:

Describing Location in a Distribution The pth percentile is the value with p percent of the observations LESS than it. (Alternate wording: p percent of observations less than or equal to it. Computing percentiles Here are 25 test scores for a class: Jenny scored an 86. How did she do on the test relative to her class? 2.Norman earned a 72. What is his percentile? 3.Janine, who scored 93, is in what percentile? 4.There are two students with scores of 80. What is/are their percentile(s)?

1.Mark receives a score report detailing his performance on a statewide test. On the math section, Mark earned a raw score of 39, which placed him in the 68 th percentile. This means that (a) Mark did better than about 39% of the students who took the test. (b) Mark did worse than about 39% of the students who took the test. (c) Mark did better than about 68% of the students who took the test. (d) Mark did worse than about 68% of the students who took the test. (e) Mark got fewer than half of the questions correct on this test. 2.Mrs. Munson is concerned about how her daughter’s height and weight compare with those of other girls of the same age. She uses an online calculator to determine that her daughter is at the 87 th percentile for weight and the 67 th percentile for height. Explain to Mrs. Munson what this means.

Although most of us buy milk by the quart or gallon, farmers measure daily milk production in pound. Guernsey cows average 39 pounds of milk a day with a standard deviation of 8 pounds. For Jersey cows the mean daily production is 43 pounds with a standard deviation of 5 pounds. When being shown at a state fair, a champion Guernsey and a champion Jersey each gave 54 pounds of milk. (a)Which cow’s milk production was more remarkable. Support your conclusions with appropriate statistical evidence. (b)What assumption do you need to make about milk production to reach your conclusion?

The distribution of batting averages for a group of baseball players is approximately normally distributed with a mean batting average of and a standard deviation of (a)What proportion of players hit between and 0.250? (b)Players in the bottom 15% of batting averages will be demoted to the minor leagues. A player will be demoted if his/her batting average below what value?

Below is a dotplot of the heights of a class of high school students along with the summary statistics from computer output. 1.Describe the distribution of heights for this class. 2.Is it reasonable to assume this distribution is normal. Use the data to support your conclusion. 3.Lynette, a student in the class, is 65 inches tall. If we can assume this distribution is normal, Lynette is in what percentile for height in this class?