Calculating Quantiles

Calculating Quantiles

Calculating Quantiles : Multi-thousand tips to make your life easier.

Descriptive statistics are never complete without using quantiles. A quantile is a piece of data that groups other data in a sequence. Calculating quantiles is helpful if you want to know how high the score of the upper 25% of a class is, or to solve similar problems. Quantiles are very flexible in statistics and are very useful for concluding what the data means.

Calculating quantiles can be a little tricky, though. There are many rules that you need to follow. Finding a quantile is not as simple as finding the sum or even the average.

Quantiles Under Different Names

Before you can calculate a quantile, you first need to know how many times you want to divide the sequence of data. There is a corresponding name depending on how many times the sequence of data will be divided:

Median - for the 2-quantile

Terciles or Tertiles (T) - for 3-quantiles

Quartiles (Q) - for 4-quantiles

Quintiles (QU) - for 5-quantiles

Sextiles (S) - for 6-quantiles

Deciles (D) - for 10-quantiles

Duodeciles (Dd) - for 12-quantiles

Vigintiles (V) - for 20-quantiles

Percentiles (P) - for 100-quantiles

Permilles (Pr) - for 1000-quantiles

Depending on what you need, choose the proper quantile type so you can divide the data evenly.

Computing Quantiles

The simplest formula to find a quantile is:

Quantile = n * (y/x)

where n is the number of data points in a sequence, y is the specific quantile, and x is the total number of quantiles. For instance, if you want to find the median of 1, 2, 3, 4, 5, and 6, you will use this formula:

Quantile = 6 * (1/2)

= 3

"6" because there are six data points in the sequence, "1" because this is the first quantile of two quantiles, and "2" because the data will be divided into two quantiles.

The answer here is "3," which means that the third number in the sequence is the point that separates the lower half from the upper half. In this sequence, that number is "3." You can say that the numbers before 3 and including 3 (1, 2, and 3) are the lower 50% of the sequence, while the numbers after 3 (4, 5, 6) are the upper 50%.

Try to calculate the quantile in a different number of parts, say four. Using the same sequence, the quartile will be found using the following figures:

Quartile = 6 * (1/4)

Notice that instead of 2, the formula is already using 4. That is because four is the total number of parts in a quartile. And so, the answer is 1.5. In this case, the answer is not an integer. Round the number to the nearest integer. Therefore, 2.

This computation means that the first 25%, or quarter, of the data includes numbers less than the second data point. In the example, the second data point (in ascending order) is 2. That means 25% of the data is made up of 1.

Automatic Quantile Computation

Take advantage of today's technology and compute quantiles automatically. There are nine quantile methods available in the R Programming Language. These methods are used to estimate quantiles.

Besides using the R Programming Language methods, you can also enter your own formula in a spreadsheet application like MS Excel. The task may be a bit more tedious, but at least it will not be as hard as manual computation.