Quartile Calculator calculates the three main quartiles of a set of numbers. Enter the set of numbers in the input field of the calculator and choose the method to be used to calculate quartiles. You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators.
Calculation of quartiles
Quartiles partition is the distribution of a sorted data set into four quarters each containing 25% of the data. Thus, each quartile is the border between two neighboring quarters of the data distribution.
The three main quartiles are as follows:
• Q1 – 1st quartile or 25th percentile – is the number that separates the lowest 25% of the data from the highest 75% of the data;
• Q2 – 2nd quartile, median or 50th percentile – is the number which is the median of the data set, so that 50% of the data lies below this number;
• Q3 – 3rd quartile or 75th percentile – is the number that separates the lowest 75% of the data from the highest 25% of the data.
Along with the minimum and maximum of the data (which are also considered quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides information about both the center and the spread of the data. Knowing the lower and upper quartile provides information on how big the spread is and if the dataset is skewed toward one side.
Another related statistic is the interquartile range, or IQR, which is the distance between the first quartile and the third quartile. The IQR is useful in calculating outliers. Any data value that is more than 1.5 times the IQR of the middle 50% of the data is called an outlier.
There is no commonly excepted agreement on selecting the quartile values for low population discrete distributions. Our Quartile Calculator uses two of the most commonly used methods.
Both methods use the median (Q2) to divide the ordered data set into two-halves. The lower quartile value (Q1) is the median of the lower half of the data and the upper quartile value (Q3) is the median of the upper half of the data.
The difference between the two methods is that when dividing the original ordered data set into two halves in the case of an odd number of data points, the first method does not include the median value of the original data set in either half, while the second method includes it in both halves. In case of an even number of data points, we split the original ordered data set exactly in half, so all the methods give the same results. Also note that in case of high population discrete distributions, the difference between all methods tends to zero.
Examples
Let’s illustrate the above with the example of the following data set: 1, 2, 3, 4, 5, 6, 7, 8, 9. It is easy to see that the median number for this dataset is 5. This means that we immediately have Q2 = 5.
Further, if we use the first method to find Q1 and Q3, then we should consider the numbers 1, 2, 3, 4 as the lower half of the data set and 6, 7, 8, 9 as the upper half of the data set. Note that the median number 5 is not included in any of these halves. It is easy to see that the median values of these two halves will be as follows: Q1 = 2.5 and Q3 = 7.5
If we use the second method to find Q1 and Q3, then the median number of 5 should be added to both halves of the original data set. That is, it is necessary to find the median values for the datasets: 1, 2, 3, 4, 5 and 5, 6, 7, 8, 9. As a result, we get: Q1 = 3 and Q3 = 7.
Now, if we consider the following data set: 1, 2, 2.3, 3, 4, 5, 6, 6.7, 7, 8, 9, we can easily get the result for both methods: Q1 = 2.3, Q2 = 4.5, Q3 = 6.7.
Related calculators
Check out our other statistics calculators such as Outlier Calculator or Standard Deviation Calculator.