5 Number Summary Calculator

5 Number Summary Calculator: Find 5 Statistical Values

The five number summary calculator is used to calculate the summary that consists of 5 statistical values, including:

• Minimum 
• First Quartile Q1
• Median Q2
• Third Quartile Q3
• Maximum 

These values are used in descriptive data analysis to understand how the large data is spread out.

What is a Five-Number Summary?

"The five number summary is a statistical measure that simplifies the key values of the dataset"

This method of summarizing data is credited to the American statistician John W. Tukey. His contribution popularized due to exploratory data analysis. While he is not alone in handling quartiles and percentiles utilized in the five-number summary, he is well known for promoting the combined use to effectively summarize data set values.

So, What are Those 5 Values?

• Minimum Value: The lowest value of the given data set
• First Quartile (Q1): This separates the lower 25% of the dataset from the upper 75%. It divides the dataset into 4 equal parts
• Median (Q2): It divides the dataset into 2 equal parts. It means that 50% of the data falls below the second quartile
• Third quartile (Q3): This is known as upper quartile means that 75% of the data values fall below the third quartile
• Maximum Value: The highest value of the given data set

Why do we Use 5 Number Summary?

A five number summary helps to summarize the large set of data values. It provides insights into the data distribution by showing the central tendency (median Q2), spread (from the quartiles i:e Q1 & Q3), and overall range (minimum and maximum values) of the dataset. 

How to Find the 5 Number Summary Step-by-Step (Manually)?

Step # 1: Arrange dataset values in ascending order from least to greatest.

Step # 2: Find the minimum value from the set of given values 

Step # 3: Find the maximum value from the given data value. 

Step # 4: Find the median;

• For odd datasets, the middle number is the median 
• For even dataset, find the average of two middle values 

Step # 5: Sort the set of values into lower and upper halves and find Quartiles;

• 1st quartile (Q1): Median of the lower half of your ordered data
• 3rd quartile (Q3): Median of the upper half of your ordered data

This 5 number summary calculator can automate the calculations but if you come for manual estimation then understanding the steps involved in the given below example can be valuable.

Solved Example (Calculate 5 Number Summary):

Let’s suppose we have a dataset 4, 10, 2, 8, 7, 15, 13

• Arrange the set of data values in ascending order = 2,4,7,8,10,13,15
• Minimum value = 2 
• Maximum value = 15 
• Median = 8
• Sort the dataset into lower and upper halves and find Q1 & Q2:
  • Lower half = 2, 4, 7
  • Upper half = 10, 13, 15
  • First quartile Q1 = median of lower half = 4
  • Third quartile Q3 = median of upper half = 13

Example (continued): Making a Box & Whisker Plot 

The whisker plot or a box plot is a visual representation used to summarize the dataset in the form of five number summary.

Where;

• The plot extend the values from 25th to 75th percentile (Q1 & Q3) 
• The median is visually represented as a line within the box. 
• The box size signifies the spread of data while the whiskers illustrate the data values outside the box. 

This five number summary calculator not only provides numerical data summaries but also creates a boxplot that identifies the outliers and visualizes data patterns. 

FAQs:

How to find the 1st quartile?

By using the below formula, you can calculate the first quartile: Q1 = (n + 1) x 1/4

Which chart is used to show five-number summary?

A box plot also known as a whisker plot used to display the 5 number summary. 

What kind of data can I use with this calculator?

This five number summary calculator lets you use numerical data sets of any size separated by commas or space to figure out 5 number summary.

What is the interquartile range?

The interquartile range (IQR) is a measure of statistical dispersion, which represents the middle 50% of a data set. It is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). The formula for calculating the interquartile range is: IQR = Q3 - Q1 Inter quartile range also be determined by using our IQR calculator. 

References:

Wikipedia: Five-number summary, Use and representation, Example

Statistics Canada: Five-number summaries