Exercise 15 Page 716

Percentiles separate data sets into 100 equal parts. The percentile rank of a data value is the percentage of data values that are less than or equal to that value. We are asked to find the values at the 30th and 90th percentiles for the given data set. 7, 12, 3, 14, 17, 20, 5, 3, 17, 4 13, 2, 15, 9, 15, 18, 16, 9, 1, 6

30th Percentile

In order to find the value that has a percentile rank of 30, we have to find the data value for which 30 % of the values are less than or equal to that value. To do so, we will first find the position of the value in the arranged list for which 30 % of the values are less than or equal to that value. First, we will multiply the number of data values by the percent written as a decimal. rl Number of Values:& 20 Percent as a Decimal:& 30 %= 0.3 Position:& 20* 0.3= 6 The value that has a percentile rank of 30 is the value in the 6^(th) position. Finally, we will arrange the values from least to greatest so that we can identify which value is the 6^(th). Arranged Values [0.5em] percentile rank of30 ↓ 1, 2, 3, 3, 4, 5, 6, 7, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20

90th Percentile

In order to find the value that has a percentile rank of 90, we have to find the data value for which 90 % of the values are less than or equal to that value. To do so, we will first find the position of the value in the arranged list for which 90 % of the values are less than or equal to that value. First, we will multiply the number of data values by the percent written as a decimal. rl Number of Values:& 20 Percent as a Decimal:& 90 %= 0.9 Position:& 20* 0.9= 18 The value that has a percentile rank of 90 is the value in the 18^(th) position. Finally, we will arrange the grades from least to greatest so that we can identify which value is the 18^(th). Arranged Values 1, 2, 3, 3, 4, 5, 6, 7, 9, 9, 12, 13 14, 15, 15, 16, 17, 17, 18, 20 ↑ percentile rank of90