Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest whole number.)18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77(a) Find the percentile of 31. th percentile(b) Find the percentile of 74. th percentile
Question
Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest whole number.)18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77(a) Find the percentile of 31. th percentile(b) Find the percentile of 74. th percentile
Solution
(a) To find the percentile of 31, we first need to determine its position in the data set. There are 32 data points and 31 appears twice, at the 11th and 12th positions. We can average these positions to get 11.5. The percentile is then calculated as (position / total data points) * 100. So, (11.5 / 32) * 100 = 35.94, which rounds to the 36th percentile.
(b) To find the percentile of 74, we see that it is the 30th data point in the set. Using the same formula as above, (30 / 32) * 100 = 93.75, which rounds to the 94th percentile.
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