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# Five Number Summary Calculator

Enter the comma separated values in the input box to find the five number summary using 5 number summary calculator.

Table of Contents:

## 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.

**1**^{st} Quartile:

^{st}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*

*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):****Find the First Quartile (Q**_{1}):**Q**_{1 }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**

**Arrange****the Data in Ascending Order =**3, 8, 10, 11, 13, 15, 16**Find the Minimum =**3**Find the First Quartile (Q**= 8_{1})**Find the Median (Q**= 11_{2})**Find the Third Quartile (Q**= 15_{3})**Find the Maximum**= 16

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

**How do you find Q**_{1} and Q_{3}?

_{1}and Q

_{3}?

**Q _{1}** (the first quartile) and

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

_{3}**Determine Q _{1}**:

- If the first half of the arranged data set has an odd number, then the middle number will be the
**1**.^{st}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
**1**.^{st}quartile - Another way to determine
**Q1**is through the approximation method, especially when dealing with large data sets:

5NumberSummaryCalculator_62

**Position for Q _{1}**:

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

**Determine Q _{3}:**

- If the second half of the arranged data set has an odd number, then the middle number will be the
**3**.^{rd}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
**3**^{rd}quartile. - Another way to determine
**Q3**is through the approximation method, especially when dealing with large data sets:

**Position for Q _{3}**:

`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`