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Sec. 2.5 β Measures of Position ___________ are numbers that partition, or divide, an ordered data set into equal parts. The three ___________ ,_______________________, approximately divide an ordered data set into four equal parts. __________ is also known as the median. The test scores of 15 employees enrolled in a CPR training course are listed. Find the quartiles of the data set. 13 9 18 15 14 21 7 11 20 5 18 37 16 17 10 The ____________________ ____________ (IQR) of a data set is the difference between the third and first quartiles. πΌππ‘ππππ’πππ‘πππ πππππ (πΌππ ) = ο· Note: One way to find outliers is to take the πΌππ β 1.5. Then subtract this quantity from π1 and add this quantity to π3 . Any data point outside this interval can be considered an outlier. What is the IQR of the CPR scores? Are there any outliers? A _______-_______________ ________________ lists the following about the data set. 1. 2. 3. What is the five-number summary for the CPR scores? 4. 5. A ___________-and- _________________ plot is a graphical way of representing a five-number summary. Create a box-and-whisker plot of the CPR scores. In addition to percentiles you can divide data into other fractiles. Fractiles Summary Symbols Divides a data set into________ equal parts. Divides a data set into________ equal parts. Divides a data set into________ equal parts. ο· If someone is in the 87th percentile for weight, then it means the person weighs more than 87% of all individuals in the _____________. ο· Note that 25th percentile = _________ 75th percentile =__________ 50th percentile =_________ You can use the following formula to find the percentile for a data point. Percentile of π₯ = Looking back at the CPR scores, what percentile corresponds to the score of 18? What percentile corresponds to the score of 20? z-score The ____________ represents the number of standard deviations a given value π₯ falls from the mean π. The formula for z-score is given below. π§= z-score example The mean speed of vehicles along a stretch of highway is 56 miles per hour with a standard deviation of 4 miles per hour. You measure the speed of three cars traveling along this stretch of highway as 62 miles per hour, 47 miles per hour, and 56 miles per hour. Find the z-score that corresponds to each speed. What can you conclude? Generally any data point more than two standard deviations away from the mean is considered unusual. Are any of these speeds in the example above considered unusual? Another example For the statistics test scores in a class the mean is 63 and the standard deviation is 7.0, and for the biology test scores in a different class the mean is 23 and the standard deviation is 3.9. A. If a student scored a 73 on the statistics test and a 26 on the biology test, then for which test did the student have the better score? B. If a student scored 63 on the statistics test and a 23 on the biology test, then for which test did the student have a better score?