# Five Number Summary Calculator

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## 5 Number Summary Calculator

Five number summary calculator is an online tool that calculates the five-number summary of the given numbers, which includes:

• Minimum Number
• Maximum Number
• First Quartile (Q1)
• Median
• Third Quartile (Q3)

Along with 5 number summary, it also finds:

• Inter Quartile
• Ascending Order
• Descending Order

## Definitions:

### Inter Quartile:

The difference between Q1 (`1st quartile`) and Q3 (`3rd quartile`) is called inter-quartile.

### 1st Quartile:

1st quartile is also known as the lower quartile, The lower quartile is a range/value in which 25% of points can be found (`when they are arranged in ascending order`)

### Ascending order:

Arrangement of numbers from the smallest to greatest number

### Descending order:

Arrangement of numbers from the greatest number to the smallest number

## How to find the five number summary?

To find the 5 number summary, follow the below example.

Example:

Find the five-number summary of the given numbers.

7, 9, 14, 3, 5, 11, 13

Step 1: Arrange the data in ascending order.

3, 5, 7, 9, 11, 13, 14

Step 2: Find the minimum and maximum number.

Minimum number = 3

Maximum number = 14

Step 3: Find the median.

Median = 9

Step 4: Find the quartiles (`Q1 and Q2`).

Q1 = median of lower half = 5

Q3 = median of upper half = 13

Step 5: Write all values to form a summary.

Minimum number = 3

Maximum number = 14

Median = 9

Q1 = 5

Q3 = 13

## FAQs

### How to calculate the five number summary?

Here's a step-by-step guide to calculate the five number summary:

• Sort the Data in Ascending Order: Arrange the data from least to greatest
• Find the Minimum: First value of the arranged data
• Find the Median (Q2): The middle value of the data set.
• Find the First Quartile (Q1): Q1 splits off the lowest 25% of data from the rest.
• Find the Third Quartile (Q3): Q3 splits off the lowest 75% of data from the rest.
• Find the Maximum: The last value of the arranged data

Example:

Find the five number summary of the given data set: 13, 11, 16, 8, 3, 15, and 10.

Solution

1. Arrange the Data in Ascending Order = 3, 8, 10, 11, 13, 15, 16
2. Find the Minimum = 3
3. Find the First Quartile (Q1) = 8
4. Find the Median (Q2) = 11
5. Find the Third Quartile (Q3) = 15
6. Find the Maximum = 16

Therefore, the 5 number summary is 3, 8, 11, 15, 16.

### How do you find Q1 and Q3?

Q1 (the first quartile) and Q3 (the third quartile) are measures of position that divide a data set into four equal parts. Here's how to determine them:

Determine Q1:

• If the first half of the arranged data set has an odd number, then the middle number will be the 1st quartile.
• If the first half of the arranged data set has an even number, Then the average of the two middle numbers will be the 1st quartile.
• Another way to determine Q1 is through the approximation method, especially when dealing with large data sets:

Position for Q1: `Position of Q1 = ​(n + 1)/4`

Determine Q3:

• If the second half of the arranged data set has an odd number, then the middle number will be the 3rd quartile.
• If the second half of the arranged data set has an even number, Then the average of the two middle numbers will be the 3rd quartile.
• Another way to determine Q3 is through the approximation method, especially when dealing with large data sets:

Position for Q3: `Position of Q3 = 3​(n + 1)/4`

### What is the interquartile range?

The interquartile range (IQR) measures the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3):

`IQR = Q3 − Q1`