Percentile Calculator
Answer:
The 64th percentile is: 220
Solution:
In this problem, you want to find the 64th percentile in the data set. At least 64% of the data values will be less than this number.
Take note that there are 15 data values in this data set. Therefore, $N = 15$.
We need to sort them in ascending order.
$ 101, 140, 142, 157, 186, 198, 200, 208, 220, 220, 228, 232, 252, 281, 287 $
The index of the sorted data set represents the position. The first number, 101 has an index of 1, the second, 140 has an index of 2, etc. To find the index of the 64th percentile, apply the formula $$ i = \frac{p}{100} \cdot N $$
where i represents the index. Substituting in the values for this problem, we have $$ i = \frac{64}{100} \cdot 15 $$ $$ i = 9.6 $$
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. $$ i = 10 $$ Counting 10 data values in the sorted data set from the beginning, the data value at position 10 is 220.
Therefore, the 64th percentile is: 220