Which Box-and-whisker Plot Represents The Data Set? 10, 5, 8, 14, 21, 7, 13, 17, 17

The procedure to abstract a ready of information that is estimated using an interval scale is called a box and whisker plot. Information technology is besides called just a box plot. These are mostly used for data interpretation.It is one of the types of graphical methods which displays the variation of the data in the dataset. We tin can besides use the histogram to brandish the data. But, histogram provides a sufficient display. Box and whisker plot is better than histogram as a box and whisker diagram volition provide additional information as information technology allows multiple sets of data to exist displayed in the same graph. In this article, yous are going to acquire what a box and whiskers plot is, how to draw a box and whisker diagram in a step by step procedure with solved examples.

Table of Contents:

Definition
Why Utilize Box and Whisker Plot?
When to Use
Stride to Draw
Example
Exercise Problems
FAQs

Box and Whisker Plot Definition

We use these box plots or graphical representation to know:

Distribution Shape
Central Value
Variability

When nosotros plot a graph for the box plot, we outline a box from the start quartile to the third quartile. A vertical line that goes through the box is the median. The whiskers (small lines) get from each quartile towards the minimum or maximum value, equally shown in the figure beneath.

$Box and Whisker plot$

A box and whisker plot is a graph that exhibits data from a five-number summary, including one of the measures of central tendency. It does not display the distribution every bit accurately every bit a stem and leaf plot or histogram does. But, it is principally used to show whether a distribution is skewed or non and if there are potential unusual observations present in the data set, which are as well called outliers. Boxplots are besides very useful when huge numbers of data collections are involved or compared.

Since the centre, spread and overall range are instantly credible, using these boxplots the arrangements can be matched easily.

A box and whisker plot is a way of compiling a set of data outlined on an interval scale. It is also used for descriptive data interpretation.

The box and whisker plot displays how the data is spread out. In the box and whisker diagram, information technology has five pieces of information, ( also called a five-number summary).

Elements of a Box and Whisker Plot

The elements required to construct a box and whisker plot outliers are given below.

Minimum value (Q ₀ or 0th percentile)

First quartile (Q ₁ or 25th percentile)

Median (Q ₂ or 50th percentile)

Third quartile (Q ₃ or 75th percentile)

Maximum value (Q _iv or 100th percentile)

Interquartile range

The meaning of each of these elements is listed below.

The minimum value in the dataset, which is displayed at the far left stop of the diagram.
The first quartile (Q₁) at the left side, which is in between the minimum value and median.
The median value, represented by the line in the middle of the box.
The third quartile (Q₃) at the right side, which is in between the median and the maximum value.
The maximum value in the dataset, which is displayed at the far correct end of the diagram.
Interquartile range (IQR) is the divergence between upper and lower quartiles, i.east. Q_iii and Q_i .

Also, read:

Quartiles
Median
Histogram
Interquartile Range

Why Exercise Nosotros Use Box and Whisker Plot?

Box and Whisker diagrams allow us to read the information very effectively and hands. Information technology summarises the data from multiple sources and displays it in a single graph. Information technology helps u.s.a. to make an constructive decision every bit it compares the data from unlike categories.

When to Use Box and Whisker Plot?

The box and whisker plot is used if we have multiple datasets from different sources which are related to each other. For example, a test score between classrooms.

How to Depict a Box and Whisker Plot?

The box and whiskers plot tin can exist drawn using five simple steps. To depict a box and whisker diagram, we need to find:

Step ane: The smallest value in the information is called the minimum value.

Pace two: The value below the lower 25% of data contained, chosen the beginning quartile.

Pace 3: Median value from the given set of data.

Step 4: The value to a higher place the lower 25% of data contained, chosen the third quartile.

Pace v: The largest value in the dataset is chosen maximum value.

Box and Whisker Plot Solved Instance

Example: Draw the box plot for the given fix of data: {3, 7, 8, 5, 12, 14, 21, 13, 18}.

Solution:

Firstly, write the given data in increasing order.

iii, 5, 7, 8, 12, thirteen, 14, 18, 21

Range = Maximum value – Minimum value

Range = 21 – iii = 18

Now, Median = eye value of the given data

Median = 12

Now, we need to find the quartiles.

First quartile = Q_ane = Median of data values nowadays at the left side of Median

Q₁ = Median of (three, 5, 7, eight)

Q₁ = (5+7)/2 = 12/2 = 6

Third quartile = Q_three = Median of data values present at the correct side of Median

Q₃ = Median of (13, 14, xviii, 21)

Q_three = (14+18)/2 = 32/2 = 16

Therefore, the interquartile range = Q₃ – Q_i = 16 – 6 = x

The five-number summary is given past:

Minimum, Q_ane, Median, Q₃, Maximum

Hence, 3, half-dozen, 12, sixteen, 21 is the five-number summary for the given data.

At present, we can draw the box and whisker plot, based on the 5-number summary.

$Box and whisker plot problem & solution$

Box and Whisker Plot Practice Issues

Solve these problems to understand the concept of the box plot.

Draw a box plot for the given set up of data {3, vii, 8, 5, 12, 14, 21, 15, xviii, xiv}.
Find the five-number summary for the given set of data {25, 28, 29, 29, thirty, 34, 35, 35, 37, 38}.

Watch The Below Video To Acquire How to Find the Median of Data

Often Asked Questions on Box and Whisker Plot

What is Box and Whisker Plot?

Box and whisker plot is one type of graphical representation which shows the five-number summary for the given ready of data, such as minimum value, lower quartile, median, upper quartile, maximum value.

Mention the advantages of Box Plot

The advantages of the box and whisker plot is that:
Nosotros can easily identify the data location and data spread.
It provides the skewness and symmetry of information
Box and whisker plot shows the information outliers.

What are the disadvantages of using Box and Whisker Plot?

The disadvantages of a box and whisker plot is that
Information technology hides the multimodality and some other characteristics of distributions.
It confuses the audition sometimes
Mean cannot be easily located.

What is meant by an outlier in a box plot?

In the box and whisker plot, some information are located outside of the box and the whisker plot, which is numerically different from the rest of the data in the dataset, is called outliers.

How to Depict Box and whisker plot?

Accommodate the data values in the ascending guild
Identify the minimum and maximum values
Observe the median of the data set
Identify the upper and lower quartile
Finally, construct the box and whisker plot