Frequency Distributions
and Histograms
Statistics: Section 2.2
Histograms

Look like bar graphs but also have the
following criteria:




The bars have the same width and always touch
The width of a bar represents a quantitative value,
such as age, rather than a category
The height of each bar indicates frequency
They give information about a range of
individuals not just a single individual.
Histograms


Your first objective is to figure out how many
bars (or classes) you want. Usually 5 to 15
groups are used.
Next, find a class width.


(range)/number of classes
Always increase to the next whole number, even if
you got a whole number as an answer.
Class Limits


The lower class limit is the lowest value in a
particular class, as the upper class limit is the
highest value in a particular class.
The class width is the difference between the
lower class limit of one class with the lower
class limit of the next class.
Midpoint (class mark)

The center of the class

[(lower class limit) + (upper class limit)]/2
Frequency Table

A frequency table lists the following:



The limits of each class
The frequency with which the data fell into a class
The class midpoint
Class Boundaries

We don’t want a space between the bars, so
we “meet halfway” between the difference of
the “lower-upper limit” and the “higher-lower
limit”.
Example: Commuting
Distance in Dallas
13
47
10
3
16
20
17
40
4
2
7
25
8
21
19
15
3
17
14
6
12
45
1
8
4
16
11
18
23
12
6
2
14
13
7
15
46
12
9
18
34
13
41
28
36
17
24
27
29
9
14
26
10
24
37
31
8
16
12
16
Example: Step 1 – Class Width

I want there to be six classes – bars
eventually.




[(largest value)-(smallest value))]/Number of
classes
If I want 6 classes
(47-1)/6 = 7.7 -> 8
So my class width is 8.
Example – Step 2: Class Limits

Determine the lower limits



Smallest value is 1 and my class width is 8.
So my lower class limits are 1, 9, 17, 25, 33, 41
Determine the upper limits


The second class begins at 9 so my upper limit for
my first class must be 8.
8, 16, 24, 32, 40, 48
Example – Step 3: Find
Midpoints

The center of the class

[(lower class limit) + (upper class limit)]/2






(1+8)/2 = 9/2 = 4.5
(9+16)/2 = 25/2 = 12.5
(17+24)/2 = 41/2 = 20.5
28.5
36.5
44.5
Example – Step 4: Find the
Class Boundaries

Extend your class limits by ½ both ways.






Class 1:
Class 2:
Class 3:
Class 4:
Class 5:
Class 6:
0.5 – 8.5
8.5 – 16.5
16.5 – 24.5
24.5 – 32.5
32.5 – 40.5
40.5 – 48.5
Example – Step 5: Create a
tally

Count how many people fall into each class
and create a bar graph from that.
Relative-frequency Histograms

Relative frequency = Class frequency / total
of all frequencies


Percentages
The graphs should look the same except the
vertical scales will be different