Find the percentile for the data value calculator

You have already learned how to calculate percentile rank, so let's move on to an actual example of calculations.

Let's say that your teacher gave back the tests from last week. You take a look at your grade (or use our test grade calculator) - it turns out that you scored 25 points, but the maximum is nowhere to be seen. You have no idea whether or not you did well on this paper. The teacher shoots you a smile and says that you need to calculate your own grade. He writes down all results on the board: 6, 12, 24, 33, 23, 17, 30, 18, 27, 17, 25, 23, 27, 20, 13, 32, 26.

The teacher also gives you the grading scale. Lo and behold, it is actually based on percentiles: grade A for percentiles 91-100, grade B for 71-90, grade C for 51-70, and D for 25-50. That's right; the teacher decided that 25% of the class would not pass the test. So, how to calculate percentile rank in this case?

1. The first thing you need to do is put the numbers in ascending order. You don't necessarily have to do it, but it will make your life much easier:

   6, 12, 13, 17, 17, 18, 20, 23, 24, 24, 25, 26, 27, 27, 30, 32, 33, which is 17 numbers in total

   We have 17 results, which means that N = 17.

2. Now, find your result. 25 points lies more or less in the final thirds of this dataset, so you start hoping for a good grade.

3. Count the results that are lower or equal to yours:

   6, 12, 13, 17, 17, 18, 20, 23, 24, 24, 25 - which is 11 numbers in total

   It means that the value of L = 11.

4. Now, all that's left to do is plug these numbers in the percentile rank formula:

   PR = L / N × 100

   PR = 11 / 17 × 100

   PR = 64.7

5. This is how to find the percentile rank, which for you is 64.7. That translates to a solid C. It could've been better, but at least you passed!

For the given set of data, the calculator will find percentile no. $$$p$$$, with steps shown.

Related calculators: Five Number Summary Calculator, Box and Whisker Plot Calculator

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Your Input

Find the percentile no. $$$25$$$ of $$$1$$$, $$$4$$$, $$$-3$$$, $$$2$$$, $$$-9$$$, $$$-7$$$, $$$0$$$, $$$-4$$$, $$$-1$$$, $$$2$$$, $$$1$$$, $$$-5$$$, $$$-3$$$, $$$10$$$, $$$10$$$, $$$5$$$.

Solution

The percentile no. $$$p$$$ is a value such that at least $$$p$$$ percent of the observations is less than or equal to this value and at least $$$100 - p$$$ percent of the observations is greater than or equal to this value.

The first step is to sort the values.

The sorted values are $$$-9$$$, $$$-7$$$, $$$-5$$$, $$$-4$$$, $$$-3$$$, $$$-3$$$, $$$-1$$$, $$$0$$$, $$$1$$$, $$$1$$$, $$$2$$$, $$$2$$$, $$$4$$$, $$$5$$$, $$$10$$$, $$$10$$$.

Since there are $$$16$$$ values, then $$$n = 16$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{25}{100} \cdot 16 = 4$$$.

Since the index $$$i$$$ is an integer, the percentile no. $$$25$$$ is the average of the values at the positions $$$i$$$ and $$$i + 1$$$.

The value at the position $$$i = 4$$$ is $$$-4$$$; the value at the position $$$i + 1 = 5$$$ is $$$-3$$$.

Their average is the percentile: $$$\frac{-4 - 3}{2} = - \frac{7}{2}$$$.

Answer

The percentile no. $$$25$$$A is $$$- \frac{7}{2} = -3.5$$$A.

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