Quartile Calculator

Quartile Calculator:

This Quartile calculator calculates the quartiles (Q1, Q2, and Q3) of the given data set, along with key statistics and a visual representation to increase understanding of the data distribution. In addition to that, it also provides:

Median
Minimum and Maximum values
Interquartile Range (IQR)
Count (Total Numbers)
Average
Geometric Mean

What Are Quartiles?

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

Q1 – Lower Quartile:

The 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. The 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. This is the difference between Q3 and Q1. For an effortless calculation of the interquartile range, access the IQR calculator and get your calculations done in seconds.

quartile

How To Calculate Quartiles?

Follow these steps:

Step #1: Order the Dataset

Arrange your data set from least to greatest value

Step #2: Count the Data Points

Calculate the number of data points (n), if you get an odd number then the center value is the median but if not then calculate the mean

Step #3: Find Q2 (The Median)

Find Q2 by splitting the given data set into two halves

Step #4: Determine Q1 (First Quartile)

Now Q1 is the median of the lower half of the data set ( if “n” is odd, then use the data points below Q2, excluding Q2)

Step #5: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data set ( if “n” is odd, then use the data points above Q2, excluding Q2)

How To Find Interquartile Range?

To find the interquartile range, subtract the value of the first quartile Q1 from the third quartile Q3.

\(\ IQR = Q3 - Q1\)

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 online quartile calculator to find quartiles instantly and see how the IQR represents the range that contains the middle 50% of the data points.

Why Do We Calculate Quartiles In Statistics?

The Quartiles are very useful in statistics because they provide an easy way to understand the spread of a data distribution. They help in:

Analyzing Data Distribution: Examining the distribution of the data around a measure of central tendency, such as the mean or median
Identifying Outliers: Calculating the extreme values that lie significantly outside the normal range of data set values
Calculating The Interquartile Range (IQR): Determining the spread of the dataset values, especially the middle 50% of data. It helps in measuring the variability of the data set values
Comparing Data Sets: Finding the differences and similarities in data set values
Generating Box Plots: Visually representing the data for a better understanding
Decision Making: Making the right investment decisions by analyzing trends, assessing risks, etc

To maximize the efficiency of your quartile and IQR calculations, consider using our statistics quartile calculator, which provides valuable insights into the distribution, spread, and potential outliers in your data.

What Is The Difference Between The Lower Quartile And The Third Quartile?

The difference between the lower and the third quartile is the interquartile range (IQR). It helps to understand the spread of the middle 50% of data.
IQR = Q3−Q1

References:
For more details, see Third Space Learning’s guide on quartiles.

To learn more about calculating quartiles, visit this Investopedia guide.

From the source of Wikipedia: Quartile.