# A test has a total score out of 150. The results achieved by the class of 17 students are listed. Calculate the percentile rank of a score of 116. Round to the nearest percent. 112, 98, 72, 77, 86, 116, 59, 103, 116, 132, 146, 125, 119, 108, 96, 122, 134

A test has a total score out of 150. The results achieved by the class of 17 students are listed. Calculate the percentile rank of a score of 116. Round to the nearest percent. 112, 98, 72, 77, 86, 116, 59, 103, 116, 132, 146, 125, 119, 108, 96, 122, 134
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Given
122,98,72,77,86,116,59,103,116,132,146,125,119,108,96,122,134
To calculate percentile rank of a score 116:
Arranging the data in ascending order,
59,72,77,86,96,98,103,108,116,116,119,122,122,125,132,134,146
Percentile rank formula is given by,
$\text{Percentile}=\left(\frac{L}{N}\right)×100$
Where L is the number of data values that are less than or equal to 116, and N is the size of the data set.
Total number of observations, N= 17
Of these 17 data values, 10 are less than or equal to the data values.
$\text{Percentile rank}=\left(\frac{L}{N}\right)×100\phantom{\rule{0ex}{0ex}}=0.5882×100\phantom{\rule{0ex}{0ex}}\text{Percentile rank}=59$
59% of the numbers in the data set have values less than or equal to 116.
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