Select Page

Reading Box-and-Whisker Plots

Home | Online Math Tutoring | 6th Grade Math Tutoring | Reading Box-and-Whisker Plots

 Box plot (also called as box and whisker plot) is a basic method to represent a given data on a graph.

We draw a rectangle on it to show the second and third quartiles, with a vertical line within to show the median value. The lower and upper quartiles are shown as horizontal lines on both sides of the rectangle. This can be drawn both horizontally and vertically.

reading box and whisker plots

Basic terms relating to graphs, box and whisker plots:

  1. Whiskers

Whiskers are spread over a wider range apart from the quartile groups. From the minimum to the maximum data represents the whisker area.

  1. Median
    The middle quartile is the mid-point of the data and is shown by the line that divides the box into two parts. This is called the median. Median is also called Quartile 2 or Q2.

Half of the data is greater than or equal to this value and half is lesser than this value.

  1. Lower Quartile or First Quartile
    It is the median of the lower half of the data set. 25% of values in the data set fall below the lower quartile (Q1) as shown in the above diagram.
  2. Upper Quartile or Third Quartile
    It is the median of the upper half of the data set. 75% of values in the data set fall below the upper quartile (Q3) as shown in the above diagram.
  3. Inter-quartile Range

The difference between the lower and upper quartiles is called as the inter-quartile range. IQR = Q3 – Q1

reading box and whisker plots

Example 1:

Find the median, quartile 1, quartile 3 for the given set of data.

9, 7, 8, 15, 14, 13, 11, 16

Solution:

Arrange the given data in ascending order: 7, 8, 9, 11, 13, 14, 15, 16

reading box and whisker plots

 For such data without range we can just split the data into respective quartiles and get the answer.

Example 2:

What is the inter quartile range of the given data set?
3, 5, 6, 9, 11, 15, 16, 18, 21, 23, 25, 27

Draw the box and whisker plot for the above data.

Solution:

Step 1: Arrange the data from least to greatest.

3, 5, 6, 9, 11, 15, 16, 18, 21, 23, 25, 27

Median of the above data is the middlemost data \left ( \frac{n +1}{2} \right )^{th} value.

We can see that, no. of items, n = 12.

Hence, median is the sum of 6th and 7th value in the given data set, divided by 2.

So, median, Q2 =\frac{15+16}{2} =\frac{31}{2}= 15.5

Lower quartile, Q1 = it’s the median value of the lower half of the data, 3, 5, 6, 9, 11, 15

Median of the above data =  \frac{6+9}{2}= \frac{15}{2}= 7.5

Upper quartile, Q3 = it’s the median value of the data set, 16, 18, 21, 23, 25, 27

Median of 16, 18, 21, 23, 25, 27 = \frac{21+23}{2}= \frac{44}{2} = 22

So, interquartile range (IQR) = Q3 – Q1 = 22 – 7.5 = 14.5

The “box” goes from Q1 to Q3, with a line drawn inside the box to show the location of the median, Q2.

Then whiskers are drawn to the endpoints (the lowest and the highest value in the given data set).

reading box and  whisker plots

 

 Note: Box and whisker plot can be drawn horizontal, as drawn above and vertical also.

Check Point

  1. The following numbers is the data of people who performed the different hours of voluntary service done in a week by teen age kids in a particular area. Find the median, and inter quartile range.

4, 6, 3, 2, 8, 5, 9, 11, 22, 13, 15, 5, 8

 

  1. From the following data

15, 20, 25, 30, 35, 40, 45, 50, 55, 60

Find the

a.Lower quartile

b.Upper quartile

c.Inter quartile range

d.Represent it graphically

Answer key
  1. Median is 8. Inter quartile range is 7.5 (IQR = Q3 – Q1 = 12 – 4.5 = 7.5)

2.

a.LQ or Q

1 = 22.5

b.UQ or Q3 = 52.5

c.IQR = 30

d.

Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved