Percentile Calculator
Answer:
The 33rd percentile is: 193
Solution:
In this problem, you want to find the 33rd percentile in the data set. At least 33% of the data values will be less than this number.
Take note that there are 16 data values in this data set. Therefore, $N = 16$.
We need to sort them in ascending order.
$ 104, 121, 132, 172, 181, 193, 195, 219, 222, 249, 255, 263, 267, 276, 279, 283 $
The index of the sorted data set represents the position. The first number, 104 has an index of 1, the second, 121 has an index of 2, etc. To find the index of the 33rd percentile, apply the formula $$ i = \frac{p}{100} \cdot N $$
where i represents the index. Substituting in the values for this problem, we have $$ i = \frac{33}{100} \cdot 16 $$ $$ i = 5.28 $$
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. $$ i = 6 $$ Counting 6 data values in the sorted data set from the beginning, the data value at position 6 is 193.
Therefore, the 33rd percentile is: 193