12.3 Measures of Central Tendency and Position 789 Two measures of position are percentiles and quartiles. There are 99 percentiles dividing a set of data into 100 equal parts; see Fig. 12.14. For example, suppose that you scored 520 on the mathematics portion of the SAT, and the score of 520 was reported to be in the 78th percentile of high school students. This wording does not mean that 78% of your answers were correct; it does mean that you outperformed about 78% of all those taking the exam. In general, a score in the nth percentile means that you outperformed about n% of the population who took the test and that about n (100 )% − of the people taking the test performed better than you did. 1 P 1 P 4 P 3 P 2 2 3 4 100 100 equal parts Percentiles Percentile indicators P 99 Figure 12.14 Example 7 Heights of 5-Year-Old Children Mrs. Judge takes her 5-year-old son to the pediatrician for a checkup. The pediatrician tells Mrs. Judge her son’s height is at the 95th percentile for 5-year-old boys. Explain what this means. Solution If a height is at the 95th percentile, it means that about 95% of the heights are below that height. Therefore, Mrs. Judge’s son is taller than about 95% of all 5-year-old boys. Also, about 5% of all 5-year-old boys are taller than Mrs. Judge’s son. 7 Now try Exercise 69. Quartiles are another measure of position. Quartiles divide data into four equal parts: The first quartile is the value that is higher than about , 1 4 or 25%, of the population. It is the same as the 25th percentile. The second quartile is the value that is higher than about 1 2 the population and is the same as the 50th percentile, or the median. The third quartile is the value that is higher than about 3 4 of the population and is the same as the 75th percentile; see Fig. 12.15. 1 2 1 4 3 4 Q1 Q 2 Q 3 Quartiles Figure 12.15 Note that a quartile is a single number, not a range of values. For example, we say a piece of data lies above or below the first quartile, but not in the first quartile. DETERMINING THE QUARTILES OF A SET OF DATA 1. List the data from smallest to largest. 2. Determine the median, or the 2nd quartile, of the set of data. If there is an odd number of pieces of data, the median is the middle value. If there is an even number of pieces of data, the median will be halfway between the two middle pieces of data. 3. The first quartile, Q ,1 is the median of the lower half of the data; that is, Q1 is the median of the data less than Q .2 4. The third quartile, Q ,3 is the median of the upper half of the data; that is, Q3 is the median of the data greater than Q .2 PROCEDURE
RkJQdWJsaXNoZXIy NjM5ODQ=