Question: The frequency distribution of the highest temperatures (in °F) in 50 states during a season is shown. Find the percentile rank for a temperature of 117.5°F by constructing a percentile graph.
Temperatures
Number of states
99.5 - 104.5
2
104.5 - 109.5
8
109.5 - 114.5
18
114.5 - 119.5
13
119.5 - 124.5
7
124.5 - 129.5
1
129.5 - 134.5
1
A ) 65th percentile B ) 55th percentile C ) 60th percentile D ) 40th percentile
Steps to derive
1 Compute the cumulative frequencies for each class (Temperature).
2 Compute cumulative percents for each class by using cumulative percent = cumulativefrequencyTotalfrequency × 100%
3 For first class, cumulative % = 250 × 100% = 4%
4 Tabulate the results
5 Draw a graph with the class boundaries on x - axis and the corresponding cumulative percents on y - axis as shown in the graph.
6 To find the percentile rank for a temperature of 117.5°F, find 117.5 on the x - axis of the percentile graph, and draw a vertical line to the graph. Then move horizontally to the value on the y - axis.
7 So, the approximate percentile rank for a temperature of 117.5°F is 60th percentile.
