Boxplot

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Lesson 5b
Graphical Displays of Data

• Boxplot
• Frequency Distribution
• Histogram

Main Ideas
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• 1. Boxplot
• A boxplot displays the median, lower and upper
  quartiles, minimum, and maximum
• The look

Median
Lower quartile
Maximum
Minimum
Upper quartile
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Example 1 Exam scores from a previous
course Exam 1 96, 79, 92, 78, 70, 87, 79,
71, 77, 82, 86, 66, 81, 50, 74, 74, 95, 91,
56, 95, 88, 59, 91 Exam 2 97, 100, 93,
71, 100, 64, 97, 82, 87, 97, 95, 92, 66,
96, 92, 93, 98, 82, 100, 93, 70, 93,
Boxplots can be used to compare the scores
from Exam 1 to Exam 2.
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Example 1 (cont) The boxplots Plots can
be used to answer questions such as a. On
which exam did students do better ? b. Which
exam had a larger spread in scores? c. Did
anyone score exceptionally well or poorly?
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• 4. 90th Percentile and Others
• The 90th percentile is the point that is greater
  than or equal to 90 of the data values.
• For instance if there are 40 observations, then
  90 of 40 is 36, so the 90th percentile would be
  the 36th from the bottom after data are put in
  order.
• Similar computation would be done for other
  percentiles.

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• Example 5. Computation of median, quartiles,
  and 90th percentile. Data are the lifetimes of
  batteries in hours.
• Data already in order (13 observations)
• 15, 17, 29, 33, 45, 89, 101, 111, 146, 155, 198,
  210, 215
• Median 101, middle number
• Quartiles 25of 13 is 3.25. Round to 3. Lower
  quartile is 3rd from bottom (29) and upper
  quartile is 3rd from the top
  (198).
• 90th percentile 90 of 13 is 11.7, rounding
  yields the 12th observation ( 210)

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• 2. Frequency distribution
• A chart that indicates the number of times,
  fraction of times, or percentage of times
  numerical values occur in a data set is called a
  frequency distribution.
• Frequency distributions may be made for
  individual numbers or for intervals of data.
• Number of students who scored 100, 99, 98, etc.
  on an exam.
• Number of students who scored between 90 and 100,
  between 80 and 89, etc.

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Example 2 . Refer to the exam scores in example
1. Suppose that a grade of A is 90-100, B is 80 -
89, etc. Frequency distributions for these
intervals which represent frequencies of various
grades are given below.
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• 3. Histogram
• A bar graph that indicates the number, fraction,
  or percentage of times numerical values occur in
  data set.
• For effective displays
• Keep intervals equally spaced.
• Dont use too few or too many interval.
• For most data sets, 5 to 10 intervals should be
  used..

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Example 3 A histogram for Exam 1
scores
Frequency
50 60 70 80 90 100

Exam Score
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How do we know which intervals to use when making
a histogram?
The choice of intervals for a histogram or
frequency distribution is subjective. There is
no one right way to do it. My experience has
shown that 5 to 10 intervals is about right in
most cases, but other than that its up to you.