What is the percentile score
You want to learn more about what a Percentile is and how do you calculate it? This article will tell you everything you need to know about it. We will first explain its meaning and then explain the calculation Step by step using a Example.
Don't feel like reading? Then check out our Videoand learn everything there about the meaning and calculation of percentiles.
What is a percentile?
A Percentile (also called percentile rank) is a Share of a distribution. You split the distribution into 100 units of equal size on. The percentile of a measured value gives you information about what proportion of the distribution is above or below this measured value. For example, if you look at the 95th percentile, that means 95% of the measured values smaller than or equal to what the 95th percentile reading is. You can calculate a percentile with this formula
Like you with the calculation need to proceed exactly, we will discuss a specific one later in this article example.
What does the 95th percentile mean?
Let's look at the example of the 95th percentile a little closer. It is particularly important in statistics and plays a role, for example Significance tests a role. Let's say you got 6 out of 7 on a task. The Distribution of scores of the other course participants can be seen in the table below.
You can see that your achieved score of 6 is the 95th percentile was assigned.
But what does that mean now?
The assignment expresses that 95% of the other course participants the same or a worse score achieved. To put it the other way around, were at the task Only 5% of the group better than you. Percentiles help us to estimate how high or low a measured value is in the comparison to the remaining values of a distribution.
Now you already know how to interpret a percentile. But before that, you often have to do it first to calculate. In a first step, you have to convert your measured values into a Ranking bring. That means you sort all values from small to large.
There are several approaches for the subsequent calculation. To choose which method is right, you have to first to calculate. corresponds to the number of measured values. stands for the percentile that you would like to calculate. Depending on whether this calculation delivers an integer result (for example "3") or a non-integer result (for example "2.5"), you have to proceed slightly differently when calculating.
n * p integer
Readings: 5 – 7 – 7 – 9 -10 -10 – 13 – 13 – 13 – 14 – 16 – 17
Let's take a look at the calculation using the series of measured values shown above. In this example we have examined 12 people and now want to determine the 25th percentile. The measured values have already been ranked in an ascending order. So in the next step we calculate directly . As you can see, we get an integer result, namely 3.
In this case, the formula to calculate the 25th percentile is:
If we insert the numbers from our example, we get:
That means 25% of the readings are less than or equal to 8.
n * p not an integer
But how do you proceed when calculating does not provide an integer result? We can also look at an example for this case.
Readings: 3 – 5 – 5 – 6 – 7 – 7 – 8 – 10 – 10
This time we have a distribution with 9 measured values and want that 20th percentile determine. We calculate as before and receive . As you can see it is 1.8 not an integer result. As a result, the formula for further calculation looks a little different:
- Percentile of
- The number between the brackets is always rounded up, regardless of how close or far it is to the next higher whole number.
The symbols mean the number between the brackets always rounded up no matter how close or far it is to the nearest whole number.
With the numbers inserted, the following calculation results:
So the 20th percentile is the second reading. So in this case it is 5.
Percentile and quantile
Finally, let's see the difference between that Percentile and the Quantileat. Both divide a distribution into several units of equal size. The term “quantile” is something, however more general as the "percentile". At Percentiles the distribution in exactly 100 units of the same size divided up. Quantiles however, can be divided into two, four or another any number of units describe. The distribution is particularly often divided into two (median), four (quartile) or 100 units (percentile). Hence the percentile is a something more precise sub-category of the quantile. If you would like to find out more details about quantiles, please have a look at our article.
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