17
Histograms
allow us to graph larger sets of data by grouping values together:
The graph above represents a sample of the heights of
31 (add the frequency of each bar)
black cherry trees.
Could we re-create the original data from this graph?
Yes
No
What is the height of the shortest measured tree?
6 0
tree h eig h t< 6 5
.
What is the height of the tallest measured tree?
8 5
tree h eig h t< 9 0
.
The graph includes the following important elements:
Descriptive title.
Properly scaled, labeled axes.
Classes
(“bars”) that are of equal width, and whose heights represent the frequency of observations for
they values (tree heights) contained in the class.
Unlike a
bar graph
, order of the bars is important.
Let’s build the h
istogram, assuming the original data was the following (sorted) heights:
60, 62, 62, 65, 67, 68, 70, 70, 71, 72, 73, 73, 73, 74, 75, 75, 75, 75, 76, 76, 77, 77, 79, 79, 82, 82, 82, 83, 84, 86, 88
Step 1:
Determine the number of
classes
(
k
) to be used.
There is no firm rule on determining this, which
means that two different people could create two valid, different histograms for the same data.
As a
guideline, count the number of observations,
n
, and take the square root of
n
.
Round
n
to the
nearest whole number and use that as the number of classes,
k
.
n
=
3 1
# of classes:
_ _ _ 6 _ _ _
k
n
(nearest whole number)
Step 2:
Determine width of each class.
Take the range (max
–
min) and divide by the number of classes,
k
.
Round this number
up to the next whole number
.
This is the class width.
Class width:
(m ax
m in )
w
k
8 8
6 0
2 8
5
6
6