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A box and whisker diagram or box plot is a visual display of some of the descriptive statistics. These statistics form the five-number summary:
The minimum value
The lower quartile
The median
The upper quartile
The maximum value
Other things to consider:
The box represents the middle 50% of the data
The lower whisker is 25% of the data
The upper whisker is 25% of the data
Box and whisker diagrams can also demonstrate skew as other statistical diagrams do.
Symmetrical
Symmetrical
The whiskers of the box plot are the same length and the median is in the centre of the box.
Positive Skew
Positive Skew
The whiskers of the box plot are the same length and the median is in the centre of the box.
Negative Skew
Negative Skew
The lower whisker is longer than the upper whisker and the median is closer to the upper quartile.
Inquiry: Explore the box plots using the Desmos activity.
Inquiry: Explore the box plots using the Desmos activity.
Example 1
Example 1
The number of hours per week that Nick worked at the Big Chicken over summer were:
5 5 4 8 10 3 12 7 7 3 8 8 15
a) Find a five-number summary for the data.
b) Represent this data on a box-and-whisker plot.
Solutions
Solutions
a) Order the data: 3 3 4 5 5 7 7 8 8 8 10 12 15
Minimum = 3
Maximum = 15
Median = 7
Lower Quartile (Q1) = 4.5
Upper Quartile (Q3) = 9
Example 2
Example 2
Solutions
Solutions
a) range = 95-25
= 70
b) Median = 60
c) Interquartile range = 75-40
=35
d i)25 is the lowest score and 75 is Q3 so 75% x 80 = 60 students had a mark between 25 and 75.
ii) 40 is Q1 and 60 is the median, so 25% x 80 = 20 students had a mark between 40 and 60.
e) 75 is the third quartile so 25% x 80 = 20 students scored more than 75.
Activity:
Activity:
Have a go at Level 2, 3 and the exam questions in the transum activity below.
Parallel Box Plots
Parallel Box Plots
Parallel box and whisker diagrams enables us to make a visual comparison about different data sets. We can easily compare the different descriptive statistics of median, interquartile range, range and skew.
Same Surface, Different Deep Questions
Same Surface, Different Deep Questions
Activity
Activity
Using the excel spreadsheet or otherwise, answer the questions below.
Parallel Box Plots.xls
Technology
Technology
Creating BoxPlots in GeGebra
In GeoGebra you can create parallel boxplots for easy comparison. Unfortunately google sheets is unable to do this easily. You. will need to download or copy over your data.
Interdisciplinary Component
Interdisciplinary Component
Complete a 5-number summary for a component of fitness relevant to your chosen sport and graph a boxplot by hand or using technology.
Write down what this shows you, what observations can you make. How might this inform your training plan?
Do you want to compare different groups or different fitness tests and could you produce stacked box plots and compare the distributions.
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