The percentile rank calculator finds the percentile rank of a number in a data set. The percentile rank of a number is the percent of values that are equal or less than that number. First, enter the data set and data value for which you want to find the percentile rank. You’ll get an answer, and then you will get a step by step explanation on how you can do it yourself.

Afterward, if you want to find a particular percentile in a data set, you can use the Percentile Formula Calculator.

### Percentile Rank Formula Calculator

### Solution:

In this problem, you want to find the percentile rank of the data value 159 in the data set. The percentile rank represents the percent of numbers in the data set that have value equal or less than 159.

Take note that there are 15 data values in this data set. It's helpful to sort them in ascending order.

$
110, 112, 118, 121, 122, 123, 129, 142, 144, 154, 159, 169, 212, 217, 251 $

Of these 15 data values, 11 are less than or equal to the data value 159. To find the percentile rank of 159, 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 159, and N is the size of the data set. Substituting in values for this problem, we have:
$$ \text{percentile rank = } (\frac{11}{15})(100) $$
$$ \text{percentile rank = } ({0.73333333333333})(100) $$

Percentile ranks are always expressed as whole numbers. Evaluating the multiplication above and rounding to the nearest whole number we have:
$$ \text{percentile rank = } {73}$$

Interpreting our answer, ** 73%** of the numbers in the data set have values less than or equal to **159**.