Exercise 4 Page 715

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 40th and 80th percentiles for the given data set. Data values 58, 53, 35, 60, 58, 42, 57, 60, 43, 44, 51, 49, 58

40th Percentile

In order to find the value that has a percentile rank of 40, we have to find the data value for which 40 % 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 40 % 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:& 13 Percent as a Decimal:& 40 %= 0.4 Position:& 13* 0.4= 5.2 The value that has a percentile rank of 40 is the value in the 5^(th) position. Finally, we will arrange the values from least to greatest so that we can identify which value is the 5^(th). Arranged values percentile rank of40 ↓ 35, 42, 43, 44, 49, 51, 53, 57, 58, 58, 58, 60, 60

80th Percentile

In order to find the value that has a percentile rank of 80, we have to find the data value for which 80 % 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 80 % 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:& 13 Percent as a Decimal:& 80 %= 0.8 Position:& 13* 0.8= 10.4 The value that has a percentile rank of 80 is the value in the 10^(th) position. Finally, we will arrange the values from least to greatest so that we can identify which value is the 10^(th). Arranged values 35, 42, 43, 44, 49, 51, 53, 57, 58, 58, 58, 60, 60 ↑ percentile rank of80