Pages

Category

# Quartile Calculator

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

## 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.