Warm Up
Develop your own Stem and Leaf Plot
with the following temperatures for
June.
77
57
67
87
80
80
50
70
80
77
82
62
62
82
68
61
65
83
65
70
65
79
59
69
73
79
61
64
76
71
Warm Up
Answer:
5
6
7
8
079
11224555789
001367799
0002237
Lesson 5: Frequency
Frequency is how often something occurs.
Example: Sam played football on…
• Saturday morning
• Saturday afternoon
• Sunday afternoon
The frequency is:
http://www.mathsisfun.com/data/frequency-distribution-grouped.html
Categorical Frequency Distribution
By counting frequencies we can make a
frequency distribution table
A categorical frequency distribution is used for
data that can be placed into specific categories.
Creating a Categorical Frequency
Distribution
Step 1:
Make a table with the following
columns in order: class, tally, and
frequency
Creating a Categorical Frequency
Distribution
Step 2:
Tally the data and place the results
in the tally column.
Creating a Categorical Frequency
Distribution
Step 3: Count the tallies and
place the results in the frequency
column.
Example Categorical Frequency Distribution
These are the favorite colors of fifteen 2nd graders.
Red
Yellow
Green
Red
Blue
Class
Blue
Red
Red
Green
Red
Tally
Green
Yellow
Red
Blue
Green
Frequency
Total=
What about if the categories of
data are numbers?
Grouped Frequency Distribution
A frequency distribution with classes that are
more than one unit in width
When the range of the data is large, the data must be
grouped into classes
41
105
109
104
57
99
112
107
105
118
67
99
87
78
101
95
125
92
Key Concept
Class Width
The class width is the range of the class.
Can be found by subtracting the lower class limit of
one class from the lower class limit of the next class
Rules For Grouped Data
Rule #1: Choose the classes
You will normally be told how many classes you need
Rule #2: Choose Class Width
ALWAYS round up to the next whole number
Rule #3: Mutually Exclusive
This means the class limits cannot overlap or be contained in
more than one class.
Rules For Grouped Data
Rule #4: Continuous
Even if there are no values in a class the class must be
included in the frequency distribution. There should be no
gaps in a frequency distribution.
(with the exception of a class with zero frequency)
Rule #5: Exhaustive
There should be enough classes to accommodate all of the
data
Rule #6: Equal Width
This avoids a distorted view of the data.
Creating a Frequency Distribution
Step 1:
Determine the minimum and maximum
values, and how many classes you need
Creating a Frequency Distribution
Step 2:
Find the class width
Class Width = __Range__
# of classes
*ALWAYS round up to the next whole number
Creating a Frequency Distribution
Step 3:
Write your minimum value as your
lowest lower limit
Minimum value
Class Limits
2
Creating a Frequency Distribution
Step 4: Add the class width to your lower
limit to find the next lower limit;
WRITE BELOW NOT BESIDE!
(do all lower limits first)
Class Limits
Ex: Class width = 9 2
11
20
29
Go until you have the amount of classes needed (in this case 4)
Creating a Frequency Distribution
Step 5: To find each upper limit, subtract
one from the next lower limit
Class Limits
2 - 10
11 - 19
20 - 28
29
Creating a Frequency Distribution
Step 6: To find last upper limit, add class
width to the 2nd to last upper limit
Class Limits
2 - 10
11 - 19
20 - 28
29 - 37
Frequency Distributions
Minutes Spent on the Phone
102
71
103
105
109
124
104
116
97
99
108 86 103
112 118 87
85 122 87
107 67 78
105 99 101
82
95
100
125
92
Make a frequency distribution table with five classes.
Minimum value =
Maximum value =
67
125
Steps to Construct a Frequency Distribution
1. Choose the number of classes
For this problem use 5
2. Calculate the Class Width
Find the range = maximum value – minimum. Then divide this by the number of
classes. Finally, round up to the next whole number.
(125 - 67) / 5 = 11.6 Round up to 12
3. Determine All Class Limits
The lower class limit is the lowest data value that belongs in a class and the upper
class limit is the highest. Use the minimum value as the lower class limit in the first
class. (67)
4. Mark a tally | in appropriate class for each data value.
After all data values are tallied, count the tallies in each class for the class frequencies.
Construct a Frequency Distribution Table
Minimum = 67, Maximum = 125
Number of classes = 5
Class width = 12
Class Limits
Tally
f
67
78
3
79
90
5
91
102
8
103
114
9
115
126
5
Do all lower class limits first.
Total=30
Try One On Your Own
After conducting a survey of 30 of your
classmates, you are left with the following set
of data on how many days off each employee
has taken this year:
7, 8, 9, 4, 10, 36, 19, 9, 26, 5,
11, 6, 2, 9, 10, 8, 16, 29, 7, 9,
8, 25, 4, 27, 8, 7, 6, 10, 34, 8
Construct a Frequency Table. Assume you want to
divide the data into 5 different classes.
Answer
Class Limits
2-8
9-15
16-22
23-29
30-36
Tally
Frequency
14
8
2
4
2
Total: 30
Homework
Frequency Table Worksheet