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Box and Whisker Plot Calculator + Online Solver With Free Steps

A Box and Whisker Plot Calculator is a simple online tool that offers a graphical depiction of data to show the median, upper provides a graphical description of data to show the data set’s median, upper quartile, and spread.

A standardized method of showing the spread of data is through this calculator.

What Is a Box and Whisker Plot Calculator?

The Box and Whisker Plot Calculator is an online tool that shows the data spread using a five-number overview: minimum value, 1st quartile, median, 3rd quartile, and the maximum value. It also goes by the name Whisker diagram.

The easiest way to display statistical information is with a box plot, which involves drawing a rectangle to symbolize the 2nd and 3rd quartiles and a vertical line within the plot to depict the median value.

Easily Use this Box and Whisker Plot Calculator to generate a Box and Whisker Plot graph. Enter a sequence of four or more values in the input field. The box and whisker plot graph will be swiftly generated for you by the calculator. Analyze one or even more clusters of data visually and efficiently with box plots. 

A box and whisker plot is a pictorial depiction of the provided cluster of data that is used in analytics. It is a unique kind of graph that displays the three quartiles, denoted by the letters Quartile 1 (Q1), Quartile 2 (Q2), and Quartile 3 (Q3). In other words, there are three quartiles into which the data can be separated.

The minimum and maximum values for the supplied data set are shown on the lines that expand from the box. It gives details on how to deal with different sets of data within the existing graph.

How To Use the Box and Whisker Plot Calculator

You can use the Box and Whisker Plot Calculator to find the desired results by following the guidelines below. You must enter the correct statistics, and the rest of the work calculator will do for you.

Step 1  

Select the method that you want to be executed on your sequence.

Step 2

Fill the entry box with the given sequence.

Step 3

To determine the Box and Whisker Plot for the provided sequence and to view the complete, step-by-step solution for the Box and Whisker Calculation, click the “Submit” button. It is an easy-to-use calculator with high accuracy and precision.

How Does a Box and Whisker Plot Calculator Work?

The Box and Whisker Plot Calculator works by combining the highest and minimum values in the sequence with the dataset’s range. Consider a series of numbers a1, a2, a3,…, an.

Let’s suppose that they are ranked from lowest to the highest for the sake of convenience. If they’re not, we would have first to place an order for them.

Also, please take note that the succeeding stages for creating a box-and-whisker plot are listed below in a distinct order than they are in the previous section. This is due to the fact that computing the five integers in the following order is typically simpler.

Maximum

The biggest number is called the maximum. Because the items in our example are arranged, we have maximal = $a_n$.

Minimum

The least significant figure is called the minimum. It is minimum = a1 in the arranged sequence.

Median

The median is a little more difficult to determine. The value that has the same amount of elements to the left and the right must be found.

If n is odd, indicating that there are such entries that are odd in number, we obtain the median as:

Median = $ \dfrac{a(n+1)}{2} $ 

The median is equal to the given equation:

Median = $ \dfrac{ \dfrac{a_n}{2} + \dfrac{a(n+2)}{2} }{2} $

But if n is even, we must take the average of both middle integers.

First Quartile

The first quartile represents the median of the entries in the lower half. However, we must once more consider n’s parity. We can easily find the median of the lower half if n is even because the sequence neatly divides into halves.

On the contrary, the 1st quartile is the median of all values from a1 up to and including  $ \dfrac{a (n+1)}{2} $ if the number n is odd, i.e., where median is defined as:

Median =  $ \dfrac{a(n+1)}{2} $

Third Quartile

The average value for the first 50 items is called the third quartile. We use the same formula as the first quartile to calculate it, but we only use half of the data. We take the values for n odd starting at  $ \dfrac{a(n+1)}{2} $  and going all the way to a (the number $ \dfrac{a(n+1)}{2} $ appears twice in the computations).

When we have all five values, it’s time to start drawing!

Solved Examples

In this section, let us solve a few examples to have a deep insight into the working of Box and Whisker Calculator.

Example 1

Imagine you’re a Professional educator at a middle school, and one day, you choose to give your pupils a 100-meter sprint test. Twenty participants in your circle take turns sprinting the distance as you record their times.

The following numbers are in order: 

13.2sec, 14.1sec, 11.9sec, 15.2sec, 14.5sec, 12.9sec, 12.7sec, 14.1sec, 18.3sec, 15.6sec, 14.5sec, 13.8sec, 12.9sec, 13.3sec, 13.9sec, 16.6sec, 15sec, 14.2sec, 17.4sec, and 16.2sec.

In addition to assigning grades to each student, you choose to assess the class’s progress as a whole. After all, drawing the box-and-whisker plot is the best method to achieve this.

Solution

We enter the data first. Although there are only eight fields accessible initially, after you start entering data, new ones appear. Additionally, note how the box plot calculator displays the solution for the first two digits and modifies the outcome and graph for each additional entry.

After entering the final one, we may scroll down to see our database’s box-and-whisker plot and 5-number summary. Let’s now look at how to create a box-and-whisker plot even without the aid of a calculator. We start by sorting the entries in accordance with the directions from the relevant section. 

In other words, we’ll be dealing with 11.9sec, 12.7sec, 12.9sec, 12.9sec, 13.2sec, 13.3sec, 13.8sec, 13.9sec, 14.1sec, 14.5sec, 14.5sec, 15sec, 15.2sec, 15.6sec, 16.2sec, 16.6sec, 17.4sec, and 18.3sec rather than the series above.

The minimum and maximum values are already known to be 11.9 sec and 18.3 seconds, respectively.

Next, we search for the median. Given that there are 20 entries—an even number—it will be the median:

$ \dfrac{(14.1s + 14.2s)}{2}$ = 14.15s 

Median is the arithmetic mean (AM) of the tenth and eleventh results.

The medians of the 1st and 2nd halves of the dataset, or the quartiles, are what we need next.

They will once more be the AMs of the fifth and sixth elements for the 1st quartile and the fifteenth and sixteenth elements for the 3rd because each has $ \dfrac{20}{2} = 10 $ entries.

Quartile 3 is given as:

$ \dfrac{(15.2s + 15.6s)}{2}$ = 15.4s 

 Quartile 1 is given as:

$ \dfrac{(13.2s + 13.3s)}{2}$ = 13.25s 

Now that we have everything we need to create a box-and-whisker plot, we can visualize our dataset.

Example 2

Find the Box and Whisker Plot of the given sequence:

55, 42, 32, 38, 50, 59, 54

Solution

32, 38, 42, 50, 54, 55, 59, in descending order

59, 55, 54, 50, 42, 38, and 32 are listed in descending order.

A maximum of 59.

A minimum of 32.

Median: 54 

Third Quartile: 55.0 

First Quartile: 38.0

Now that we have everything we need to create a box-and-whisker plot, we can visualize our dataset.

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