Percentile Calculator
Answer:
The 46th percentile is: 163
Solution:
In this problem, you want to find the 46th percentile in the data set. At least 46% of the data values will be less than this number.
Take note that there are 13 data values in this data set. Therefore, $N = 13$.
We need to sort them in ascending order.
$ 102, 125, 130, 133, 143, 163, 167, 175, 175, 188, 222, 252, 281 $
The index of the sorted data set represents the position. The first number, 102 has an index of 1, the second, 125 has an index of 2, etc. To find the index of the 46th percentile, apply the formula $$ i = \frac{p}{100} \cdot N $$
where i represents the index. Substituting in the values for this problem, we have $$ i = \frac{46}{100} \cdot 13 $$ $$ i = 5.98 $$
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 163.
Therefore, the 46th percentile is: 163