Percentile Calculator
Answer:
The 55th percentile is: 213
Solution:
In this problem, you want to find the 55th percentile in the data set. At least 55% of the data values will be less than this number.
Take note that there are 17 data values in this data set. Therefore, $N = 17$.
We need to sort them in ascending order.
$ 107, 112, 121, 140, 148, 179, 181, 198, 211, 213, 228, 231, 239, 270, 278, 282, 284 $
The index of the sorted data set represents the position. The first number, 107 has an index of 1, the second, 112 has an index of 2, etc. To find the index of the 55th percentile, apply the formula $$ i = \frac{p}{100} \cdot N $$
where i represents the index. Substituting in the values for this problem, we have $$ i = \frac{55}{100} \cdot 17 $$ $$ i = 9.35 $$
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 213.
Therefore, the 55th percentile is: 213