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Box-and-Whisker Plots

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on 19 October 2014

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Transcript of Box-and-Whisker Plots

What is it?
Box-and-Whisker plots are a way to show data, visually, along a number line, by using
medians
in the data. The data is divided into
four equal parts
, and these equal parts are called
quartiles
.
They are drawn
above
a number line that displays from the least value to the greatest.
Definitions
Quartiles - certain points that divide the data set into 4 equal parts

Five-Number Summary - the five numbers that make up the box-and-whisker plot (least value, first quartile, median, third quartile, and greatest value)

Interquartile Range - the difference of the third quartile and first quartile (middle half of data)
Shapes of the Plots
Skewed Left
- when the left whisker is
longer than the right whisker, when most of the data is on the right
Shapes Cont.
Skewed Right
- when the right whisker is longer than the left whisker, when most of the data is on the left
Box-and-Whisker Plots
Anna Nguyen
June 10, 2014
Algebra
Parts of the Plot
First Quartile
Median
Third Quartile
Greatest Value
Least Value
Left Whisker
Right Whisker
Shapes Cont.
Symmetric
- when the whiskers are about the same length, when the median is in the middle of the data
Example Problem #1
Interpret It!
Example Problem #2
Compare It!
1. Order the data
2. Find the median of the whole set of data, then the middle value of both the upper and lower half of the data
3. Make a number line that includes the least and greatest values and plot the five-number summary above it.
4. Draw a box using the quartiles (median=second quartile). Draw a vertical line down the median and horizontal lines from the box to the end points (whiskers)
The range is 8.
10-2=8
10 is the greatest value
2 is the least value
25% of the data are between 2 and 5.
50% of the data are between 5 and 8.5.
25% of the data are between 8.5 and 10.
The interquartile range is 3.5.
8.5 - 5 = 3.5
8.5 is the third quartile
5 is the first quartile
You are comparing the hours of TV that two small classes watch daily during summer vacation. The responses are listed below.
1. Order the both data sets (separately)
2. Find the median of the whole set of data, then the middle value of both the upper and lower half of the data (do this to both sets)
3. Make a number line that includes the least and greatest values and plot the five-number summary above it. (they should be plotted on the same number line)
4. Draw a box using the quartiles (median=second quartile). Draw a vertical line down the median and horizontal lines from the box to the end points (do this to both plots)
Both of the plots are skewed right because for each one, the right whisker is longer and the data is mostly on the left side of the graph.
The results from class #2 are more spread out than the results from class #1. Class #2 has a greater range than class #1. The interquartile range is also longer than class #1.
The range of Class #1 is 7 (7-0=7).
The range of Class #2 is 8 (9-1=8).
Class #1 - 0, 1, 2, 3. 3, 4, 5, 6, 7
Class #2 - 1, 1, 1, 1, 2, 2, 3, 8, 9
What was Learned:
Box-and-Whisker Plots are a different way to represent data

There are 3 shapes to the plots (skewed left, skewed right, and symmetric)

Plots are recorded above the number line

The different ways to interpret and compare box-and whisker plots
Full transcript