Warm UpDevelop your own Stem and Leaf Plot with the following temperatures for June.

77 80 82 68 65 59 6157 50 62 61 70 69 6467 70 62 65 65 73 7687 80 82 83 79 79 7180 77

Warm UpAnswer:

5 0 7 96 1 1 2 2 4 5 5 5 7 8 97 0 0 1 3 6 7 7 9 98 0 0 0 2 2 3 7

Frequency is how often something occurs.

Example: Sam played football on… • Saturday morning• Saturday afternoon• Sunday afternoon

The frequency is:

Lesson 5: Frequency

http://www.mathsisfun.com/data/frequency-distribution-grouped.html

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.

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.

Creating a Categorical Frequency Distribution

Class Tally Frequency

Total=

Example Categorical Frequency Distribution

These are the favorite colors of fifteen 2nd graders.RedYellowGreenRedBlue

BlueRedRedGreenRed

GreenYellowRedBlueGreen

What about if the categories of data are numbers?

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

Grouped Frequency Distribution

41 104 112 118 87 95105 57 107 67 78 125109 99 105 99 101 92

Class Limits: The values which determine the upper and lower limits of a class

Lower Class Limit: Smallest data value that can be included in the class

Upper Class Limits: Largest data value that can be included in the class

Key Concept

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

Class Width

Rule #1: Choose the classesYou will normally be told how many classes you need

Rule #2: Choose Class WidthALWAYS round up to the next whole number

Rule #3: Mutually ExclusiveThis means the class limits cannot overlap or be contained in more than one class.

Rules For Grouped Data

Rule #4: ContinuousEven 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: ExhaustiveThere should be enough classes to accommodate all of the data

Rule #6: Equal WidthThis avoids a distorted view of the data.

Rules For Grouped Data

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

Class Limits2Minimum value

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 Limits2Ex: Class width = 9

112029

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 Limits2

112029

- 10- 19- 28

Creating a Frequency Distribution

Step 6: To find last upper limit, add class width to the 2nd to last upper limit

Class Limits2

112029

- 10- 19- 28- 37

Creating a Frequency Distribution

Frequency Distributions

102 124 108 86 103 82 71 104 112 118 87 95103 116 85 122 87 100105 97 107 67 78 125109 99 105 99 101 92

Make a frequency distribution table with five classes.

Minutes Spent on the Phone

Minimum value =Maximum value =

67125

4. Mark a tally | in appropriate class for each data value.

Steps to Construct a Frequency Distribution

1. Choose the number of classes

2. Calculate the Class Width

3. Determine All Class Limits

For this problem use 5

Find the range = maximum value – minimum. Then divide this by the number of classes. Finally, round up to the next whole number.

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)

After all data values are tallied, count the tallies in each class for the class frequencies.

(125 - 67) / 5 = 11.6 Round up to 12

Total=30

78

90

102

114

126

35

8

9

5

67

79

91

103

115

Do all lower class limits first.

Class Limits Tally f

Construct a Frequency Distribution TableMinimum = 67, Maximum = 125Number of classes = 5Class width = 12

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:

Construct a Frequency Table. Assume you want to divide the data into 5 different classes.

Try One On Your Own

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

AnswerClass Limits Tally Frequency

2-8 149-15 8

16-22 223-29 430-36 2

Total: 30

Frequency Table Worksheet

Homework