Quartile Calculator

Quartile Calculator

Quartile calculator is a tool that helps to find the quartiles of the data set values. You just need to enter the set of values separated by a comma or space 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?

Quartiles are the statistical values that divide the dataset into four equal parts. There are three quartiles (Q1, Q2, and Q3) that create a four interval. Each of them contains roughly 25% of the data points.

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. This quartile 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. Quartile Q2 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.

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.