Histograms
Lecture 18
Sec. 4.4.4
Tue, Feb 17, 2004
Histograms

Histogram – A display of continuous
quantitative data in which the data are
divided into classes and rectangles
represent the frequencies of the
classes.
Drawing Histograms


Use Data Set 1 on p. 184.
Find the maximum value, the
minimum value, and the range.
Maximum = 51
 Minimum = 32
 Range = Max – Min = 51 – 32 = 19.

Drawing Histograms


Divide the data into classes of equal
width.
The classes must not overlap.
Choose a convenient starting point.
 Choose a convenient class width.
 Write the endpoints of each class.

Drawing Histograms



Starting point = 30.
Class width = 5.
Classes:
30
 35
 40
 45
 50

up
up
up
up
up
to
to
to
to
to
35 (but not including 35).
40.
45.
50.
55.
Drawing Histograms


We may denote the classes in either of
two ways.
Interval notation: [low, high)
[30, 35),
 [35, 40),
 [40, 45), etc.
 [ and ] mean “include endpoints.”
 ( and ) mean “exclude endpoints.”

Drawing Histograms

Range notation: low – high
30 – 34,
 35 – 39,
 40 – 44, etc.
 This notation does not indicate whether the
endpoints are included.
 Therefore, be sure the endpoints do not
overlap.

Drawing Histograms

Count the number of observations in
each class. This is the frequency of
the class.
Class
Frequency
[30, 35)
1
[35, 40)
2
[40, 45)
8
[45, 50)
7
[50, 55)
2
Drawing Histograms



Draw horizontal and vertical axes.
On the horizontal axis, show the class
boundaries.
On the vertical axis, show uniform
reference points representing
frequencies apropos to the data.

For example, 0, 2, 4, …
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms

Over each class, draw a rectangle
whose height is the frequency of that
class.
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Drawing Histograms
Frequency
8
6
4
2
Age
0
30
35
40
45
50
55
Guidelines

Never use too few or too many classes.




Usually 5 to 12 classes is about right.
Use simple round numbers for the class
boundaries.
Mark off the vertical axis uniformly, showing
regular reference points, not the actual
frequencies.
Frequencies must start at 0.
Let’s Do It!


Let’s do it! 4.14, p. 224 – Histogram of
Household Income.
Let’s do it! 4.16, p. 226 – Matching
Shapes to Characteristics.
Example

See Example 4.10, p. 227 – Histogram
versus Bar Graph.
Histograms on the TI-83


See page 263 for more detailed
instructions.
Enter the data into list L1.


{45, 41, 51, …, 37}  L1
Press STAT PLOT
Turn Plot1 On.
 Select Histogram Type.
 Specify List L1.

Histograms on the TI-83

Press WINDOW
Set
 Set
 Set
 Set
 Set


Xmin to the starting point.
Xmax to the last endpoint.
Xscl to the class width.
Ymin to 0.
Ymax to the maximum frequency.
Press GRAPH

The histogram appears.
Frequency Distributions
on the TI-83

After getting the histogram, press
TRACE.
The display shows the first class and its
frequency.
 Use the left arrow to see the other class
frequencies.

Assignment


Page 227: Exercises 30 – 38.
Page 249: Exercises 68, 69.