# A quick overview of Five Number Summary and its Calculations

Data summarizing is a quick and simple method of explaining all of the values in a data collection using only a few statistical statistics. The mean and standard deviation are used to describe data with a Gaussian distribution, but if your data collection does not have a Gaussian distribution, they may be useless or even incorrect.

We will show you how to utilize a five-number summary to summarize the distribution of a data sample without assuming a complex data distribution in this post. This statistics summary can be used for any form of data analysis.

After reading this post, you will be able to use data summarization techniques such as estimating the mean and standard deviation, which are exclusively applicable to the Gaussian distribution. In addition, you will be able to identify a data sample using a five-number summary.

### Five Number Summary – Definition

A non-parametric data summation method is the five-number summary. It’s also known as the five number summary because it comprises five statistical phrases that we’ll go over later.

It is generally referred to as the Tukey 5 number summary because it was proposed by John Tukey. It can be applied to any type of data to characterize the distribution of test samples.

As a normal summary, the five number summary contains just the proper amount of information. The following are the five terms of the five number summary.

### 1st Quartile Q1

The first quartile is produced by taking the median of the data set’s lower half. It shows us that 25% of the numbers in the data set are below the first quartile and approximately 75% are above it. Q1 is the symbol used to represent it.

### 2^{nd} Quartile or Median Q2

The median is a statistical figure that indicates the data set’s most middle value. In other words, the median separates the bottom half of a data set from the upper half.

### 3^{rd} Quartile Q3

The third quartile is found by calculating the median of the data set’s upper half. It shows us that 75% of the numbers in the data set are below the third quartile and 25% are above it. Q3 is the symbol used to represent it.

### Maximum

A maximum number is the number in the data set with the highest value. It is the most significant number in a given set of data.

### Minimum

A minimum number is the number in the data set with the lowest value. It’s the smallest number in a given set of numbers.

## When should you use Five Number Summary?

Data summarizing approaches enable you to explain data distribution using only a few primary measurements.

The most general example of data summarization is the calculation of the mean and standard deviation for data having a Gaussian distribution. Using only these two characteristics, you can comprehend and replicate the data distribution. The data summary may include as little as tens of individual findings or as many as billions.

The problem is that measuring the mean and standard deviation of data that does not have a Gaussian distribution is challenging. These quantities are mathematically calculable, however they do not summarize the data distribution. In truth, they can be extremely deceptive.

Try out five number summary calculator to find all of the values associated with this term.

In the absence of a Gaussian distribution, the five-number summary should be employed to summarize the data set.

## Creating Five Number Summary step by step

When we compare the procedure of computations to the entire collection of data we generally have with us, calculating a 5-number summary is simple. As previously explained, we must calculate five statistical terms in order to provide a five-number summary of our data.

Here, we’ll provide an example to show how the procedure works. For clarity, each term will be calculated separately. Before we get into the computations, here’s a hint for finding a five-number summary.

**Example:**

Make use of the following data set.

3, 4, 6, 2, 7, 1, 12

**Solution:**

- The first step is to always arrange the data set. Sort the values in ascending order using a least to greatest calculator.

1, 2, 3, 4, 6, 7, 12

- Determine the lowest and highest possible number. Because the data set is structured in ascending order in this example, you can simply choose the first number as the lowest and the last value as the maximum.

**12** is the maximum number.

**1** is the minimum number in this data set.

- Determine the median. Begin removing elements from both sides of the data set one by one. The median will be the remaining value at the end. If the data collection has an even number of values, add the final two remaining values and divide by two to get the median.

1, 2, 3, **4,** 6, 7, 12

4 is the median.

- Determine the 1st quartile by calculating the upper half’s median. Quartile calculator can assist you when calculating quartiles in a big way.

1, 2, 3 is the upper half in this case.

1^{st} Quartile = 2

- Determine the 3rd quartile by calculating the lower half’s median.

6, 7, 12 is the lower half in this case.

3^{rd} Quartile = 7

- Make a list of all the values to represent the 5-number summary.

1^{st} Quartile |
2 |

3^{rd} Quartile |
7 |

Median | 4 |

Maximum Number | 1 |

Minimum Number | 12 |

## Wrapping it up

A quartile is an observable number at a certain moment that aids in the division of an ordered data sample into four equal-sized bits. The median, or second quartile, divides the ordered data set in half, whereas the first and third quartiles divide each half in thirds.

A percentile is an observed value at a certain point that aids in the segmentation of a structured data sample into 100 equal-sized portions. Quartiles are frequently expressed as percentages.

The quartile and percentile values are also rank statistics that may be calculated on any data set. They are used to quickly characterize how much data in the distribution is behind or ahead of a specific observed value.