Histograms
Please view this tutorial and answer the
follow-up questions on loose leaf to
turn in to your teacher.
Histogram Basics
• A statistical graph that measures the
frequency of a set of data
• The x-axis can be set up as intervals of one or
more depending on the values of the data
• The y-axis always represents frequency (how
often a value or range of values occurs)
Example
Station
Anchorage, AK
Mobile, AL
Los Angeles, CA
Atlanta, GA
Des Moines, IA
Boston, MA
Helena, MT
Buffalo, NY
Philadelphia, PA
Houston, TX
Milwaukee, WI
July High
Temperature
(oF)
65
91
84
88
87
82
85
80
86
93
80
What will be the title on
your x-axis?
The x-axis should be labeled
“Temperature (oF)” because
each value in the list is a
high temperature.
Example
Station
Anchorage, AK
Mobile, AL
Los Angeles, CA
Atlanta, GA
Des Moines, IA
Boston, MA
Helena, MT
Buffalo, NY
Philadelphia, PA
Houston, TX
Milwaukee, WI
July High
Temperature
(oF)
65
91
84
88
87
82
85
80
86
93
80
Why shouldn’t the names of
the cities included on the xaxis?
Because the x-axis
represents the range of
temperatures not the
specific temperature for
each city.
NEVER include categories as
labels for the x-axis of a
histogram!
Set up your title and labels
July High Temperatures (oF)
5
The temperatures range from
65 to 93. What should be the
minimum and scale for the xaxis?
Frequency
4
3
The y-axis ALWAYS measures
frequency and should ALWAYS
start at zero and count by
ones.
2
1
0
60
65
70
75
80
85
Temperatures (oF)
90
95
Adding Data to the Histogram
July High Temperatures (oF)
5
Frequency
4
The bar between 65 and 70
goes up to 1 on the y-axis
because there is only one
value (65) in this range.
Values on a
tick mark are
counted in the
bar to the
right!
3
2
How high will the bar be
between 80 and 85?
1
0
60
65
70
75
80
85
Temperatures (oF)
90
95
Adding Data to the Histogram
July High Temperatures (oF)
5
Frequency
4
3
Correct! The bar
between 80 and 85
will go up to 4 on the
y-axis.
Here is the
completed
histogram.
2
1
0
60
65
70
75
80
85
Temperatures (oF)
90
95
Shapes of Histograms
Skewed to the right – tail
is on the right
Bimodal – two peaks
Skewed to the left – tail
is on the left
Symmetric – mirror
image on both sides
Analyzing the Histogram
July High Temperatures (oF)
5
Which shape best
represents our
histogram?
Frequency
4
3
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
Analyzing the Histogram
July High Temperatures (oF)
5
Frequency
4
Skewed to the left!
Notice that the tail is
on the left.
3
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
Analyzing the Histogram
July High Temperatures (oF)
5
What is the minimum
and maximum value
in our data set?
Frequency
4
3
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
65 is the minimum
and 95 is the
maximum.
Analyzing the Histogram
If you said 80-90 is the
max, you want to
think about the
largest value on the xaxis that has a bar
touching it.
July High Temperatures (oF)
5
Frequency
4
3
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
For the minimum, you
want to find the
smallest value that is
touching a bar (not
the smallest value on
the x-axis).
Analyzing the Histogram
Is there a peak in this
data set? If so, where?
July High Temperatures (oF)
5
Frequency
4
3
The peak for this data
set is between 80 and
90 with a frequency of
4. It is the highest
point in the graph.
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
Analyzing the Histogram
5
Frequency
4
3
Are there gaps in the
histogram? If so,
where are they?
July High Temperatures (oF)
Gaps MUST have a
beginning and an
end.
There is one gap from
70 to 80 in this data
set.
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
60 to 65 is not a gap
because there is no
bar before 60.
Analyzing the Histogram
Are there any outliers
in this data set? If so,
where and why? If
not, why not?
July High Temperatures (oF)
5
Frequency
4
3
2
1
0
60
65
70
75
80
85
o
Temperatures ( F)
90
95
There are no outliers
(unusually high or low
values) because the
bar at 65 to 70 is only
two spaces away.
A bar must be at least 3 spaces away from the rest of the data
to be considered an outlier.
Now It’s Your Turn!
• Use what you’ve just reviewed to help you
answer the following questions.
• Submit any graphs on graph paper along with
answers to each question to your teacher.
(These do not need to be included on the
wikispace!)
High School Graduation Rates for the 50 United States
by Percentage
58
55
76
63
87
65
75
70
62
63
58
80
85
62
58
75
70
57
89
78
65
85
71
71
90
72
76
83
73
76
74
68
83
67
72
66
58
65
76
76
53
72
75
71
80
58
74
83
54
78
Make a histogram of the data. Remember to include all
important information. Once you’ve completed the histogram,
move on to the next slide to answer some questions.
Follow-Up Questions
1.
2.
3.
4.
Describe the shape of the histogram.
What are the minimum and maximum?
What is the peak of the histogram?
Are there any gaps in the histogram? If so,
where. If not, why not.
5. Are there any outliers in the histogram. If so,
where. If not, why not.
Follow-Up Questions
20
18
16
Frequency
14
12
6. Describe the
distribution of this
histogram using as many
descriptors as possible.
10
8
6
4
2
0
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