The data is 2, 7, 15, 16, 26, 27, 31, 34, 37, 41, 44, 45, 48, 51, 53, 57. Find the 41st percentile.
41% of n = 0.41(16) = 6.56. If you do not get a whole number, as in this case, you round up to the next whole number, 7. Then the 7th value is the 41st percentile. The 41st percentile is 31.
Note that you get 31 corresponding to the 41st and 43rd percentile. This sort of thing can happen with small data sets. You would need to have al least 100 values for all the percentile ranks to be different.
Now find the 50th percentile: Find 50% of n = 0.5(16) = 8. When you get a whole number, in this case 8, you take the average of the eighth and ninth values = (34 + 37)/2 =35.5. The 50th percentile is 35.5
Note that you should find 50% of values less that the 50th percentile and 50% of values more that the 50th percentile, or at least as close as it is possible. In other words the 50th percentile is the same as the median. You can check in this example that this is indeed the case.