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Quartile Calculator

Free quartile calculator. Paste a data set to get Q1, median, Q3, the interquartile range, and outliers, using the textbook or Excel method.

Separate numbers with commas, spaces, or new lines. You can paste a spreadsheet column.

Interquartile range (IQR)

28

Q1 15 · Q2 40 · Q3 43

Sorted data

6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

Summary statistics

Count (n)
11
Sum
365
Mean
33.181818
Median
40
Mode
No mode (no value repeats)
Minimum
6
Maximum
49
Range
43
Q1
15
Q3
43
IQR
28
Sample std. deviation
15.873362
Population std. deviation
15.134657
Sample variance
251.963636

How it's calculated

Sort the data, then:

For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 the median of halves gives Q1 = 15, Q2 = 40, Q3 = 43, so IQR = 28.

Welcome to our free quartile calculator! Simply enter your data set in the calculator above. If you don’t know what it means to be in a particular quartile, read our introduction to the calculator below. If you need the use of other statistics based calculators, check out our mean, mode and median calculators.

Quartiles are a significant aspect of statistics and are extensively used for data analysis, especially in the field of descriptive statistics. Essentially, quartiles are values that divide a dataset into four equal parts or quarters. They are the three points (Q1, Q2, and Q3) that split the data set into four equal groups. The first quartile (Q1) is the middle value between the smallest value and the median of the data set, the second quartile (Q2) is the median of the data, and the third quartile (Q3) is the middle value between the median and the highest value of the data set. By partitioning data into quartiles, we can easily identify and understand the spread and center of the data, outliers, and whether the data is skewed.

Quartiles are important in various statistical calculations. They are most notably used in the calculation of the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The IQR is a measure of statistical dispersion and is commonly used to build box plots for visual data representation. Quartiles are also used in outlier detection; any data point that falls below Q1 – 1.5_IQR or above Q3 + 1.5_IQR is generally considered an outlier. Quartiles are also handy in comparing the distribution of data points across different data sets. For instance, in business, they can be used to compare sales data across different quarters or regions.

How To Use Our Quartile Calculator

Enter your data

In the text input box labeled “Enter numbers separated by commas,” input your data set. Each number must be separated by a comma. For instance, if your data set consists of the numbers 1, 2, 3, 4, and 5, you would enter “1,2,3,4,5” into the box.

Click “Calculate”

After entering your data, press the button labeled “Calculate Quartiles”. The calculator will then process the data you entered, sorting it in increasing order and determining the quartile values.

View the results

After the calculations have been done, the results are displayed on the same page under the button. The first quartile (Q1), the second quartile or median (Q2), and the third quartile (Q3) are displayed. These values divide your data into four equal parts, allowing you to understand the spread of your data better.

Frequently Asked Questions

›What are quartiles?

Quartiles split sorted data into four equal parts. Q1 has 25% of values below it, Q2 is the median (50%), and Q3 has 75% below it.

›What is the interquartile range (IQR)?

IQR = Q3 − Q1. It is the spread of the middle half of the data and, unlike the full range, is not affected by extreme values.

›Why do different calculators give different quartiles?

There are several accepted methods. The textbook method takes the median of each half of the data; Excel’s QUARTILE.INC interpolates between values. They agree on large data sets but can differ on small ones, so this calculator lets you choose.

›How are outliers found?

With Tukey’s fences: any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged as an outlier.

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