Percentile Calculator


Answer:

The 61th percentile is: 180


Solution:

In this problem, you want to find the 61th percentile in the data set. At least 61% of the data values will be less than this number.

Take note that there are 18 data values in this data set. Therefore, $N = 18$.

We need to sort them in ascending order.

$ 102, 104, 108, 126, 131, 153, 155, 161, 163, 167, 180, 201, 210, 213, 218, 250, 254, 268 $

The index of the sorted data set represents the position. The first number, 102 has an index of 1, the second, 104 has an index of 2, etc. To find the index of the 61th percentile, apply the formula $$ i = \frac{p}{100} \cdot N $$

where i represents the index. Substituting in the values for this problem, we have $$ i = \frac{61}{100} \cdot 18 $$ $$ i = 10.98 $$

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. $$ i = 11 $$ Counting 11 data values in the sorted data set from the beginning, the data value at position 11 is 180.

Therefore, the 61th percentile is: 180