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Quartile calculator

Quartile Calculator

Use this statistical tool to calculate the quartiles (q1, q2, & q3) for the data set.

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Quartile Calculator

This quartile calculator helps to calculate and organize your data set into different quartiles. You just need to enter the values and let this calculator find statistical values to understand how data is distributed:

  • Lower Quartile (Q1) 
  • Median Quartile (Q2)
  • Upper Quartile (Q3)
  • Interquartile range (IQR)
  • Average 
  • Geometric mean
  • Total sum
  • Population standard deviation
  • Sample standard deviation
  • Range 
  • Count (Total numbers)
  • Graph to represent Quartiles

What are Quartiles?

Quartile is a statistical term that divides the data set into 4 equal parts. There are three quartiles (lower quartiles Q1, median quartiles Q2, and upper quartiles Q3), creating four divisions.

Q1 – Lower Quartile

Lower quartile (Q1) shows the 25th percentile of the data set. This means that 75% of the data points fall above it. It is a point that separates the group with a ratio of 1:3

Q2 – Median Quartile

The median quartile means that the data is divided in half with 50% falling below and 50% falling above. It is a point that splits the group with a ratio of 2:2

Q3 – Upper Quartile

The upper quartile means the 75% percentile of the given dataset. It means 75% of data falls below Q3 and the remaining 25% falls above it. This point separates the group into 3:1

Interquartile Range (IQR)

IQR is the analysis to determine how the values are spread in the middle 50 % ‍ of a dataset. It is the difference between the Q3 and the Q1. This can also be calculated with the help of an IQR calculator.

quartile calculator

Quartiles Formula

These are formulas that help for calculating quartiles yourself:

Lower Quartile = \(\ Q1 = (n + 1) \times{\frac {1}{4}}\)

Median Quartile = \(\ Q2 = (n + 1) \times{\frac {2}{4}}\)

Upper Quartile = \(\ Q3 = (n + 1) \times{\frac {3}{4}}\)

Interquartile Range = \(\ IQR = Q3 – Q1\)

How To Calculate Quartiles?

  • Order your data set from least to greatest value 
  • Calculate the number of data points (n)
  • Find Q2 that splits the given data set into two halves
  • Q1 is the middle value of the lower half of the data set
  • Q3 is the middle value of the upper half of the data set

Let us show these calculations with the example:

For the given set of data 2, 7, 9, 11, 13, 23, and 16 find the quartiles and interquartile range.

Step 1: Order the data

2, 7, 9, 11, 13, 16, 23

Step 2: Calculate the total number of terms n

Total terms (n) = 7

Here’s how to find the positions of the quartiles:

Step 3: Lower Quartile

\(\ Q1 = (n + 1) \times{\frac {1}{4}}\)

\(\ Q1 = (7 + 1) \times{\frac {1}{4}}\)

\(\ Q1 = 2\)

In the given data set the second value is 7

Step 4: Median Quartile

\(\ Q2 = (n + 1) \times{\frac {2}{4}}\)

\(\ Q2 = (7 + 1) \times{\frac {2}{4}}\)

\(\ Q2 = 4\)

In the given data set the fourth value is 11

Step 5: Upper Quartile

\(\ Q3 = (n + 1) \times{\frac {3}{4}}\)

\(\ Q3 = (7 + 1) \times{\frac {3}{4}}\)

\(\ Q3 = 6\)

In the given data set the sixth value is 16

Interquartile Range (IQR)

\(\ IQR = Q3 – Q1\)

\(\ IQR = 16 – 7\)

\(\ IQR = 9\)

You can also put the same values in the quartile calculator to find quartiles and how the IQR represents the range that contains the middle 50% of the data points.