The percentile formula calculator will find the score for the desired percentile for a data set. First, enter the data set and desired percentile and you’ll get the answer. Then, you will get a step-by-step explanation on how to do it yourself. The desired percentile represents the percent of numbers in the data set that have values at or below the number that we’ll calculate.

Afterward, see the Percentile Rank Calculator if you have a score and need to find its percentile rank. You GOT this!

### Answer:

The 20th percentile is: **137**

### Solution:

In this problem, you want to find the 20th percentile in the data set. At least 20% of the data values will be less than this number.

Take note that there are 14 data values in this data set. Therefore, $N = 14$.

We need to sort them in ascending order.

$
106, 121, 137, 153, 184, 187, 225, 239, 251, 261, 261, 285, 286, 287 $

The **index** of the sorted data set represents the position. The first number, 106 has an index of 1, the second, 121 has an index of 2, etc. To find the index of the 20th percentile, apply the formula
$$ i = \frac{p}{100} \cdot N $$

where **i** represents the index. Substituting in the values for this problem, we have
$$ i = \frac{20}{100} \cdot 14 $$
$$ i = 2.8 $$

If i were an integer, the percentile would be found by taking the average of the data values at positions i and i + 1 in the sorted data set. Since i is not an integer in this problem, we round i **up** to the nearest whole number.
$$ i = 3 $$
Counting 3 data values in the sorted data set from the beginning, the data value at position 3 is 137.

Therefore, the 20th percentile is: **137**