Box and Whisker Plots
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Box and Whisker Plots
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Box and Whisker Plots. This data shows the scores achieved by fifteen students who took a short maths test. The test was marked out of ten. To construct a box and whisker plot, we need five pieces of information. The median. The lower quartile. The upper quartile. The lowest value. - PowerPoint PPT Presentation
Transcript of Box and Whisker Plots
Box and Whisker Plots
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This data shows the scores achieved by fifteen students who took a short maths test. The test
was marked out of ten.
To construct a box and whisker plot, we need five pieces of information.
The median
The highest value
The lowest value
The upper
quartile
The lower
quartile
To find the median and the upper and lower quartiles, we first of all need to arrange the data….
in rank order
0
0 1
0 1 2
0 1 2 2
0 1 2 2 3
0 1 2 2 3 3
0 1 2 2 3 3 3
0 1 2 2 3 3 3 4
0 1 2 2 3 3 3 4 4
0 1 2 2 3 3 3 4 4 4
0 1 2 2 3 3 3 4 4 4 5
0 1 2 2 3 3 3 4 4 4 5 6
0 1 2 2 3 3 3 4 4 4 5 6 7
0 1 2 2 3 3 3 4 4 4 5 6 7 8
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The median value is the value thn 12
1
where n is the number of data items, so here, n = 15.
The median value is the 8th value which is 4
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The median value is the value thn 12
1
where n is the number of data items, so here, n = 15.
The median value is the 8th value which is 4
median
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The lower quartile is the value thn 14
1
where n is the number of data items, so here, n = 15.
The lower quartile is the 4th value which is 2
median
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The lower quartile is the value thn 14
1
where n is the number of data items, so here, n = 15.
The lower quartile is the 4th value which is 2
medianl.q.
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The upper quartile is the value thn 14
3
where n is the number of data items, so here, n = 15.
The upper quartile is the 12th value which is 6
medianl.q.
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The upper quartile is the value thn 14
3
where n is the number of data items, so here, n = 15.
The upper quartile is the 12th value which is 6
medianl.q.
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The upper quartile is the value thn 14
3
where n is the number of data items, so here, n = 15.
The upper quartile is the 12th value which is 6
medianl.q. u.q.
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medianl.q. u.q.
The lowest value is 0
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
medianl.q. u.q.
The lowest value is 0
The highest value is 9
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
medianl.q. u.q.
The lowest value is 0
The highest value is 9
Now that we have found the median, both quartiles
and the highest and lowest values, we have all the information which we need in order to be able to
construct the box and whisker diagram
We first of all need some sort of grid. We can use graph paper for this or just ordinary squared
paper will do equally well
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medianl.q. u.q.
First of all we draw the box
Data
For this, we will need to provide a scale which should be clearly
labelled
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medianl.q. u.q.
0 1 2 3 4 5 6 7 8 9 10
Data
Scores out of ten
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
medianl.q. u.q.
Next we draw the whiskers
0 1 2 3 4 5 6 7 8 9 10
Data
Scores out of ten
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9 10
Data
Scores out of ten
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
The Box and Whisker Plot is complete
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Data
Scores out of ten
0 1 2 2 3 3 3 4 4 4 5 6 7 8 9
And the final diagram looks like this
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Data
Scores out of ten
0 1 2 3 4 5 6 7 8 9 10
Scores out of ten
Box and Whisker plots are useful when comparing sets of data
For instance, the scores of the original group of students, group A are now being compared with those of a second group B
Group A
Group B
Box and Whisker plots are useful when comparing sets of data
For instance, the scores of the original group of students, group A are now being compared with those of a second group B
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Scores out of ten
Group A
Group B
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Scores out of ten
By simply examining the two side by side box and whisker plots, we can easily deduce lots of useful information.
For instance………
Group A
Group B
The highest score was in group B
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Scores out of ten
Group A
Group B
The lowest score was in group A
0 1 2 3 4 5 6 7 8 9 10
Scores out of ten
Group A
Group B
On average, group A did better
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Scores out of ten
Group A
Group B
The top 50% of students in group A did better than the bottom 75% of students in group B
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Scores out of ten
Group A
Group B
In group A, the middle 50% of the students scores were between 2 and 6 inclusive whereas with group B, the middle 50% of the students scores were contained in a narrower range of values between 2 and 4
inclusive.
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Scores out of ten
Group A
Group B
We could say a great deal more about these two diagrams
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Scores out of ten
But now it’s your turn to draw and interpret some
Box and Whisker diagrams of your own
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A Box and W hisker P lot to show the m ock exam m arks of three m aths A level sets
A
B
C
Set
Exam Score (% )
