### Percentile Calculator

### Answer:

The 52nd percentile is: **166**

### Solution:

In this problem, you want to find the 52nd percentile in the data set. At least 52% of the data values will be less than this number.

Take note that there are 10 data values in this data set. Therefore, $N = 10$.

We need to sort them in ascending order.

$ 112, 119, 120, 121, 127, 166, 183, 216, 254, 293 $

The * index* of the sorted data set represents the position. The first number, 112 has an index of 1, the second, 119 has an index of 2, etc. To find the index of the 52nd percentile, apply the formula
$$ i = \frac{p}{100} \cdot N $$

where **i** represents the index. Substituting in the values for this problem, we have
$$ i = \frac{52}{100} \cdot 10 $$
$$ i = 5.2 $$

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 166.

Therefore, the 52nd percentile is: **166**