Advantages & Disadvantages of Box Plots

Report
Warm-Up
Joshua, a sophomore at Hoover High School, usually goes to bed
around 11:00 p.m. and gets up around 8:00 a.m. to get ready for
school. That means that he gets about 9 hours of sleep on a
school night. He decided to investigate this statistical question:
How many hours per night do sophomores usually sleep when
they have school the next day?
Joshua surveyed 20 sophomores. The following data set
represents the average number of hours each student sleeps on a
school night:
{                  9 }
Make a dot plot, histogram, and box plot to display the data.
Check point!
Who would you have surveyed to
answer the statistical question?
Which graph best illustrates the
data?
The Statistical Process…
 is a problem-solving process consisting of four steps:
1. formulating a statistical question that
anticipates variability and can be answered by
data.
2. designing and implementing a plan that
collects appropriate data.
3. analyzing the data by graphical and/or
numerical methods.
4. interpreting the analysis in the context of the
original question.
Variables
 Read the following statistical questions and determine
whether the question is categorical or numerical.
a. Do professors of math get paid more than professors of
science?
b. Do women live longer than men?
c. What is the language most commonly spoken at home
amongst people in South Florida?
d. What is the length of students’ feet in Ms. Moe’s class?
e. What is the favorite sport of students at Majorly High
School?
f. What is the post code of students that attend Flamingo
Middle School?
Why is some data that
contain numbers, such as
the post codes, considered
categorical?
Types of Graphs:
 Dot Plot
 Histogram
 Box Plot
Dot Plot
 A dot plot is a graphic display using dots and a simple
scale to compare the frequency within categories or
groups.
Dot Plot(continued)
 A dot plot is useful for relatively small sets of data.
 Dot plots clearly display clusters/gaps of data and
outliers.
 In dot plots, the frequency axis is not necessary
but you need to count to find the frequency in
each stack of dots, and they can be hard to
construct and interpret for data sets with many
points.
 They can be used with numerical and categorical
data.
Histogram
 A histogram is a type of graph that shows the
frequency distribution of data within equal intervals
(thus, there are no spaces between the bars).
Histogram(continued)
 It shows the number of values within an interval and
not the actual values.
 You can graph huge data sets easily with histograms.
 They are used only for numerical data.
 You could change the intervals of the histogram to see
which gives a better description of the data.
Box-Plots
 The box plot is a standardized way of displaying the
distribution of data based on the minimum, first
quartile, median, third quartile, and maximum of the
data set.
Box-Plots(continued)
 A box plot is a good way to summarize large amounts
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of data.
It displays the range and distribution of data along a
number line.
Box plots provide some indication of the data’s
symmetry and skew-ness.
Box plots show outliers.
Original data is not clearly shown in the box plot; also,
mean and mode cannot be identified in a box plot.
They can be used only with numerical data.
Remember:
 Graphs must always be clearly labeled.
 Changing the scales in a graph can make the
data look very different, ultimately changing
the impression that the graph makes.
 When comparing two or more sets of data,
the scales must be consistent; otherwise, it
is difficult to compare the data.
What Graph Would You Choose?
The following lists different hypothetical data sets.
Which graphical representation would best illustrate
the data? Explain.
 Comparison of the annual snow fall between two
snowboarding resorts over several years.
 The amount of time spent watching TV, in hours, of
200 participants.
 Wind speed at a windmill farm over a three-week
period.
 Students’ favorite summertime activity.

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