Five-Number Summary Calculator

To efficiently condense your dataset into a concise statistical summary, our Five-number summary calculator is an ideal resource. It enables you to determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum, providing a quick insight into the distribution and range of your data.

What is a Five-Number Summary?

A Five-number summary is a set of five descriptive statistics that provide insights into your dataset’s spread, central tendency, and variability.

It is widely used in data analysis, statistics, and the creation of box plots.

The five components are:

1. Minimum (Min): The smallest data value.

2. First Quartile (Q1): The median of the lower half of the dataset (25th percentile).

3. Median (Q2): The middle value of the dataset (50th percentile).

4. Third Quartile (Q3): The median of the upper half of the dataset (75th percentile).

5. Maximum (Max): The largest data value.

This summary helps you quickly understand the distribution of your dataset, especially if it’s skewed or contains outliers.

Formulas of Five-Number Summary Calculator

In this section, we provide the necessary formulas to calculate the five-number summary for your dataset.

1. For Minimum and Maximum Values: To find the minimum and maximum values, sort the dataset in either ascending or descending order. If arranged in ascending order, the first value is the minimum, while the final value is the maximum. Conversely, in descending order, the first value is the maximum, and the last value is the minimum.

2. For First Quartile: To determine the first quartile, extract the lower half of the sorted dataset and find the median of that segment. The first quartile represents 25% of the dataset. The formula for the first quartile is:

First Quartile = {(n+1)/4}th term

3. For Median: If the total number of terms of the data set is odd, then:

                              Median = {(n+1)/2}th term

And, if the total number of terms of the data set is even, the formula for the median is:

                                       Median = {(n/2)th term + (n/2+1)th term}/2

4. For Third Quartile: To find the third quartile, you simply take the top half of the sorted dataset and determine the median of that upper half. The third quartile represents 75% of the overall dataset. The formula for calculating the third quartile is:

  Third Quartile = {¾(n+1)}th term

Here, n = number of values in a dataset.

Example of a Five-Number Summary

Let’s try and understand with the help of an example:

Dataset:
7, 10, 13, 15, 18, 21, 22, 25, 28, 30

Here, n = 10

• Minimum (Min) = 7
  
• Maximum (Max) = 30
  
• Median (Q2) = {(n/2)th term + (n/2+1)th term}/2 = 19.5
  
• Q1 = {(n+1)/4}th term = 13
  
• Q3 = {¾(n+1)}th term = 25
  

5-Number Summary = 7, 13, 19.5, 25, 30

How to Find the Five-Number Summary Using Our Calculator

• Enter the values separated by a comma, a space, or a new line.
• Click “Calculate” and the tool automatically sorts and computes all five summary values.

Conclusion

The Five-number summary calculator is an essential statistical tool for quickly understanding any dataset’s structure. By knowing your minimum, quartiles, median, and maximum, you can easily detect outliers, understand skewness, and visualize data distribution effectively.