Percentile Rank Formula Calculator
Solution:
In this problem, you want to find the percentile rank of the data value 179 in the data set. The percentile rank represents the percent of numbers in the data set that have value equal or less than 179.
Take note that there are 14 data values in this data set. It's helpful to sort them in ascending order.
$ 107, 124, 139, 153, 153, 164, 179, 191, 196, 206, 221, 233, 255, 282 $
Of these 14 data values, 7 are less than or equal to the data value 179. To find the percentile rank of 179, apply the formula: $$ \text{percentile rank = } (\frac{L}{N})(100) $$ where L is the number of data values that are less than or equal to 179, and N is the size of the data set. Substituting in values for this problem, we have: $$ \text{percentile rank = } (\frac{7}{14})(100) $$ $$ \text{percentile rank = } ({0.5})(100) $$
Percentile ranks are always expressed as whole numbers. Evaluating the multiplication above and rounding to the nearest whole number we have: $$ \text{percentile rank = } {50}$$
Interpreting our answer, 50% of the numbers in the data set have values less than or equal to 179.