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Listed are 29 ages for Academy Award winning best actors
in order from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
x = 18 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{18+0.5(1)}{29}$ (100) = 63.80. 58 is the 64 ^{th} percentile.
x = 3 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{3+0.5(1)}{29}$ (100) = 12.07. Twenty-five is the 12 ^{th} percentile.
Listed are 30 ages for Academy Award winning best actors in order from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31, 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
Find the percentiles for 47 and 31.
Percentile for 47: Counting from the bottom of the list, there are 15 data values less than 47. There is one value of 47.
x = 15 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{15+0.5(1)}{29}$ (100) = 53.45. 47 is the 53 ^{rd} percentile.
Percentile for 31: Counting from the bottom of the list, there are eight data values less than 31. There are two values of 31.
x = 15 and y = 2. $\frac{x+0.5y}{n}$ (100) = $\frac{15+0.5(2)}{29}$ (100) = 31.03. 31 is the 31 ^{st} percentile.
A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. Percentages of data values are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15 ^{th} percentile.
A percentile may or may not correspond to a value judgment about whether it is "good" or "bad." The interpretation of whether a certain percentile is "good" or "bad" depends on the context of the situation to which the data applies. In some situations, a low percentile would be considered "good;" in other contexts a high percentile might be considered "good". In many situations, there is no value judgment that applies.
Understanding how to interpret percentiles properly is important not only when describing data, but also when calculating probabilities in later chapters of this text.
When writing the interpretation of a percentile in the context of the given data, the sentence should contain the following information.
On a timed math test, the first quartile for time it took to finish the exam was 35 minutes. Interpret the first quartile in the context of this situation.
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