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Table of Content
 1 What is the five number Summary? 2 How to find 5 number summary (Step-By-Step)? 3 When the Summary doesn’t exist? 4 What do quartiles tell us? 5 Is the First Quartile the same as the 25th percentile?
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An online 5 number summary calculator helps to find the five number summary of data set that includes minimum, $$Q1$$, $$Q2$$ (median), $$Q3$$, and maximum. When it comes to analyzing a large (but finite) data set, it is crucial to know how its elements are distributed.

Apart from 5-point summary, this five number summary calculator allows you to find different other characteristics that help you in data set element distributions.

Well, if your concerned to know how to find 5 number summary values (step-by-step), then you reached the exact place. It’s time to read on to get an appropriate idea of data set distribution values according to the summary.

## What is the Five Number Summary?

The five-number summary is useful in the descriptive statistics or during the preliminary investigation of a large data set, but infinite. The five-number summary can be defined in statistical values that are presented together and ordered from lowest to highest. Let’s we define these values individually:

• The minimum: it is the smallest value in any given data set. It is denoted by $$Q0$$.
• The First Quartile: It is represented by $$Q1$$ and $$25%$$ of total data falls below it. Lower quartile, Lower hinge, and $$25th$$ percentile are some other names to represent it in 5 number summary stats.
• The Median: It represents the midpoint of the whole data $$.50%$$ of total data falls below it. It is also known as the second quartile $$Q2$$.
• The Third Quartile: $$Q3$$ represents it and $$75%$$ of total data falls below it. The upper quartile, upper hinge, and $$75th$$ percentile also represent it.
• The Maximum: It is the largest value in any data set.

Example:

If a data set is $$“1,2,3,4,5,6″$$, then to find the five number summary you to look for:

• The minimum: $$1$$
• The median: $$\frac {3 + 4} {2} = 3.5$$
• The maximum: $$6$$.
• $$Q1$$: It is $$2$$ that is also the median of $$1,2,3$$.
• $$Q3$$: it is $$5$$ that is also the median of $$4,5,6$$.

A 5 number summary calculator is the easiest way to avoid the burden of manual calculations. Furthermore, it also minimizes the risk of error and saves your time. For convenience, you could try the free mean median mode range calculator that find the central tendency & statistical measurements of the data set.

## How to Find 5 Number Summary (Step-By-Step)?

When you find the five number summary of data you will have a rough idea about any given data set. For instance, you’ll have the lowest number and the highest number. The main reason to find it is to figure out more useful statistics, like the interquartile ranges. Even though a Five number summary calculator can give you the results within seconds but by following some simple steps you can figure it out manually as well.

Step 1:

First of all, you have to arrange your data in ascending order. For example: $$1, 2, 3, 6, 7, 10, 13, 15, 18, 19, 30$$.

Step 2:

In the second step you have to find the minimum and maximum value of the data set. In the given data set the minimum is $$1$$ and the maximum is $$30$$.

Step 3:

Now you have to find the median. It is the middle number of your data. You can place the parentheses around the numbers that are above and below the middle number. It will be your median.

• $$(1, 2, 3, 6, 7)$$$$, 10,$$ $$(13, 15, 18, 19, 30)$$ in this data $$10$$ is the middle number.

Step 4:

The middle number divides the data into two sets. The one is $$(1, 2, 3, 6, 7)$$ and the other is $$(13, 15,18,19,30)$$. To find the $$Q1$$ you have to look for the median of first set that is $$3$$ and to find the $$Q3$$ you have to look for the median of second data set that is $$18$$.

Step 5:

In the final step you just have to write down the summary of your data. Minimum $$= 1$$, $$Q1 = 3$$, $$Median = 10$$,$$Q3 = 18$$, and $$Maximum = 30$$.

You must try this free quartile calculator to figure out the $$Q1, Q2, Q3$$, and IQR range from the data set.

### Examples:

There are different means to address the question that how to find five number summary of the data. Some of them are explained below:

Example 1:

To find the 5-number summary for $$0, 0, 1, 2, 11, 13, 21, 19$$ you have to follow simple steps:

• First of all, we will arrange the data: $$0, 0, 1, 2, 11, 13, 19, 21$$
• Meanwhile, there are total of $$8$$ observations. So the median will be the average of the $$4th$$ and $$5th$$ value: $$\frac {2+11}{2}=6.5$$.
• The minimum value is $$0$$.
• The highest value is $$21$$.
• The middle of the first or lower half is $$\frac {0+1}{2} = 0.5$$
• The middle of the second or upper half is $$\frac {13+19}{2} = 16$$
• Therefore, the five number summary will be $$0, 0.5, 6.5, 16, 21$$.

Example 2:

If the five number summary is given you can easily create a data set as follows:

$${1, 5, 9, 18, 20}$$

Assume that there are total $$8$$ values. The minimum value will be $$1$$ and the maximum value will be $$20$$. Now the two middle points should be average to be $$9$$ so they be $$8$$ and $$10$$. The second and third values should be average to $$5$$ so they might be $$4$$ and $$6$$. Now the $$6$$ and $$7$$ points need to be average to be $$18$$ one possible data set can be: $$2, 4, 6, 8, 10, 18, 18, 20$$

Example 3:

Now if the given data set is $$“1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 10, 15”$$. How will you calculate its 5-number summary?

Such complex data set can be summarized by using a 5 number summary calculator but manual calculations will be as follows:

• There are total $$20$$ values in the set.
• The minimum number is $$1$$.
• $$Q1$$ will be $$2+32=2.5$$. $$Q2$$ can be calculated by taking average of $$4+52=4.5$$.
• Meanwhile, the $$Q3$$ is the average of $$6+72=6.5$$.
• The maximum number is $$15$$.

Example 4:

The data set is: $$2, 8, 10, 11, 13, 14, 16, 18, 21, 30$$. First of all divide the data into two equal halves.

• Minimum number is $$4$$
• $$Q1$$ is $$10$$. It is the middle of first half.
• $$Q2: \frac {13+15} {2} =14$$. It is the half of whole data.
• $$Q3$$ is $$18$$. It is the middle of second half.
• Maximum number: $$30$$

The five number summary is $$4, 10, 14, 18, 30$$.

Example 5:

Data set is “$$1, 7, 9, 14, 18, 19, 22, 27, 99$$”. There are total $$9$$ values. For the calculations $$Q1$$ and $$Q3$$, you have to include the median in both the lower half and upper half of the data.

Minimum value is $$1$$.

• $$Q1$$ is $$9$$ as is the middle number of first half.
• $$Q2$$ is $$18$$ as it is the middle of whole data.
• $$Q3$$ is $$22$$ as it is the middle of second half of data. (this is the median of $$19, 19, 23, 27, 29$$)
• Maximum is $$99$$. Therefore, a five number summary will be $$1, 9, 18, 22, 99$$.

However, a five number summary calculator give this summary in the blink of an eye and you won’t have to divide the data into two halves.

## How to Use Five number summary calculator?

The 5 number summary calculator demonstrates 5 fragments along with other statistical characteristics of any given data set.

Input:

• To calculate 5 number summary, you have to enter numerical data that should be separated with comma or space.
• Click the calculate button.

Output:

The 5-point summary calculator will find:

• 5 Number Summary including (Minimum, Quartile $$Q1$$, Quartile $$Q2$$ (median), Quartile $$Q3$$, Maximum)
• Statistical Characteristics including (Interquartile Range, Average, Geometric Mean, Total Sum, Population Standard Deviation, Sample Standard Deviation, Range, Count of Total Numbers, Ascending Order and Descending Order of the data set
• Last of all it will display a box and whisker chart to visually represent the data set.

## When the Summary doesn’t exist?

Sometimes, it becomes impossible to find a five-number summary. For the five numbers to exist, any data should meet two requirements:

Univariate: Data should be univariate. It means that data must be a single variable. For example, this list of pounds is one variable: $$120, 100, 130, 145$$. On the other hand, if there is a list of age and you need to compare it with pounds then such data will be known as bivariate as not it is including two variables. Such pairs make it impossible to find a five number summary of data.

Specific Order: Data set should be an ordinal, interval, or ratio. Otherwise, it would be impossible to figure out the five number summary. For using The 5 number summary calculator you need to meet these two requirements first.

## Box and Whisker Chart:

A box and whisker chart demonstrates the visual distribution of data into quartiles. It also highlights the mean and outliers of the data. Such boxes also have some lines that are extending vertically and known as “whiskers”. Such lines specify variability that may exist outside the upper and lower quartiles. Any point that exists outside the whiskers will be recognized as outliers.

## FAQ’s:

### What do quartiles tell us?

Quartiles explain the division of any data set by breaking it into different sets. It simply demonstrates the average of your data more precisely. Furthermore, five number summary generator gives detail of quartiles along with other statistical divisions of the data set.

### Is the First Quartile the same as the 25th percentile?

Quartiles are kind of special percentiles. The first quartile of any data will be equivalent to $$25th$$ percentile. In the same way and the third quartile will be equal to $$75th$$ percentile. On the other hand, the median is called the $$50th$$ percentile.

### Are 100 percentiles possible?

If there is a “percentage below or equal to” then, yes, you can possibly have the $$100th$$ percentile. As for percentiles, there are total $$99$$ equal partitions from $$1$$ to $$99$$. It is inconsiderate to say there are $$100$$ equal percentile bands while making percentiles calculations.

## Takeaway:

This 5 number summary calculator, provides you the chance to learn and practice of how to find the 5 number summary of any dataset. Whenever you are analyzing a large set of data and want to know the precise distribution of its elements, this is the place that you should turn to first. The tool presents that data in the form of a neat statistical chart along with a graphical representation. Well, give it a try and find out!

## References:

From the legitimate source of Wikipedia: Complete Guide of 5 (Summary)

From the source of thought (co): What is a statistical summary of 5 number, find!

Get the information from mathbits: about 5 statistical summary