Percentile Calculator
Answer:
The 65th percentile is: 225
Solution:
In this problem, you want to find the 65th percentile in the data set. At least 65% of the data values will be less than this number.
Take note that there are 12 data values in this data set. Therefore, $N = 12$.
We need to sort them in ascending order.
$ 103, 116, 131, 144, 153, 153, 154, 225, 276, 283, 293, 296 $
The index of the sorted data set represents the position. The first number, 103 has an index of 1, the second, 116 has an index of 2, etc. To find the index of the 65th percentile, apply the formula $$ i = \frac{p}{100} \cdot N $$
where i represents the index. Substituting in the values for this problem, we have $$ i = \frac{65}{100} \cdot 12 $$ $$ i = 7.8 $$
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. $$ i = 8 $$ Counting 8 data values in the sorted data set from the beginning, the data value at position 8 is 225.
Therefore, the 65th percentile is: 225