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3.8 Box and Whiskers

It is one step further to stem-and-leaf. It displays a number of statistics like, median, lower quartile (Q1), upper quartile (Q3), Inter-quartile range (IQR). It tells us about the symmetry of the distribution and also gives us the idea about the highest and the lowest values.

Verbal GMAT scores of 12 students 10, 22, 24, 27, 31, 33, 39, 40, 42, 43, 44, 45

Solution: The scores is arranged in the ascending order. 10,                 22, 24, 27, 31, 33, 39, 40, 42, 43, 44, 45

    1)   Since n = 12 ( total items )
     The two middle scores are = 6th and = 7th.

      i.e. 33 and 39 respectively.

     Therefore the average of the two is the median

      i.e. Median =

   2)   The quartile (Q1) is the median of the bottom half. i.e.
         25th percentile.


   3)   The upper quartile (Q3) is the median of the top half. i.e.
        75th percentile.

Now the box-plot is constructed as follows:-
 i)    The line inside the box indicates the median.
 ii)   The left side of this box indicates the lower quartile (Q1).
 iii)   The right side of this box indicates the upper quartile
 iv)   A straight line is then drawn from the lowest value of this
       distribution through the box to the highest value of this
       distribution. This horizontal straight line is called the


3.1 Introduction
3.2 Comparison Between Tabular And Diagrammatic Presentation
3.3 Difference Between Diagrams And Graphs
3.4 General Principles Of Constructing Diagrams
3.5 Bar Diagrams
3.6 Pie Chart
3.7 Graphs
3.8 Box and Whiskers

Chapter 4

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