1. Frequency Distribution
A table with categories or classes
and counts of how many data in each
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2. Is your data Qualitative or Quantitative?
Qualitative: it’s a category
Blood type
Model of car
Favorite fast food restaurant
Quantitative: it’s a numerical measurement
Heart rate, beats per minute
Fuel efficiency, miles per gallon
Dollars spent on meal, or 0-10 satisfaction scale
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3. Frequency Distribution for Categorical Data
Category
Frequency
Cumulative Frequency
Relative Frequency
(list the categories here in this column)
(put the counts of how many in this column)
(sum the counts as you progress from row to row)
(this category is what percent of the total sample size?)
(What order? High to low?
Low to high? Alphabetical? It’s your design decision.)
Observation: The Family Feud game board is a categorical frequency distribution.
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4. Categorical (or, Qualitative) Frequency Distribution example
“What state did you visit most recently?”
State visited (the category)
How many (the frequency)
Alabama 71
California 18
Florida
138
New York 7
South Carolina 48
Tennessee 27
Texas 53
Other states 70
TOTAL
432
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5. Things we do with Categorical Frequency Distributions
We draw pictures of them – a future lesson
Bar graphs
Pie charts
Cutesy repeated icons variation of the bar graph
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6. Quantitative Frequency Distribution (data is number measurements)
Classes
Frequency
Each class is a low-to-high range of values
These are called the “Class Limits”
The frequency column gives a count of how many data values fit in the class
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7. Quantitative Frequency Distribution (data are number measurements)
Placement Test Score
How many applicants
Cumulative frequency
0-9 19
10-19 38 57
20-29 52
109
30-39 71
180
40-49 50
230
50 and above 28
258
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8. About the Quantitative Frequency Distribution
Instead of individual test score values, we GROUPED data into CLASSES
Classes are sometimes called “bins” or “buckets”
Each class is a low-to-high range of data values
Each data value falls into exactly one class
May be one or two “open-ended”classes
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9. About the classes CLASS LIMITS are 10-19, 20-29, etc.
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About the classes
CLASS LIMITS are 10-19, 20-29, etc.
Classes do not overlap!
Classes are usually the same width.
CLASS MIDPOINTS are like 14.5, 24.5, etc. (High minus low, divided by 2)
CLASS BOUNDARIES split the “gap” between class limits: , , etc.
“ ” means 9.5 ≤ x < (note ≤ vs. < )
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10. Comprehensive example
The slides in this background color are taken from the publisher’s slides to accompany Bluman’s textbook.
Some corrections and some edits may have been made.
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11. Rules Guidelines for Classes in Grouped Frequency Distributions
There should be 5-20 classes.
The class width should be an odd number.
The classes must be mutually exclusive.
The classes must be continuous.
The classes must be exhaustive.
The classes must be equal in width (except in open-ended distributions).
Bluman, Chapter 2

12. Remarks on Bluman’s rules
There should be 5-20 classes.
[Johnson & Kuby, 10th Edition, page 57 says “The square root of n is a reasonable guideline for the number of classes with samples of fewer than 125 data values.”]
2. The class width should be an odd number.
[JK10 also says “When it is convenient, an even class width is often advantageous.” !!!]
Bluman, Chapter 2

13. Remarks on Bluman’s rules
The classes must be equal in width (except in open-ended distributions).
But how about classes for Income ?
Income Range
Frequency
Percent of total
$0 - $9,999
$10,000 - $29,999
$30,000 - $59,999
$60,000 - $149,999
$150,000 - $499,999
$500,000 and up
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14. Constructing a Grouped Frequency Distribution
The following data represent the record high temperatures for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes.
Bluman, Chapter 2

15. Constructing a Grouped Frequency Distribution
STEP 1 Determine the classes.
Find the class width by dividing the range by the number of classes 7.
Range = High – Low
= 134 – 100 = 34
Width = Range/7 = 34/7 = 5
Rounding Rule: Always round up if a remainder.
Bluman, Chapter 2

16. Constructing a Grouped Frequency Distribution
For convenience sake, we will choose the lowest data value, 100, for the first lower class limit.
The subsequent lower class limits are found by adding the width to the previous lower class limits.
Class Limits
100 -
105 -
110 -
115 -
120 -
125 -
130 -
The first upper class limit is one less than the next lower class limit.
The subsequent upper class limits are found by adding the width to the previous upper class limits.
104
109
114
119
124
129
134
Bluman, Chapter 2

17. Constructing a Grouped Frequency Distribution
The class boundary is midway between an upper class limit and a subsequent lower class limit. 104,104.5,105
Class Limits
Class Boundaries
Frequency
Cumulative Frequency
Bluman, Chapter 2

18. Constructing a Grouped Frequency Distribution
STEP 2 Tally the data.
STEP 3 Find the frequencies.
Class Limits
Class Boundaries
Frequency
Cumulative Frequency 2 8 18 13 7 1
Bluman, Chapter 2

19. Constructing a Grouped Frequency Distribution
STEP 4 Find the cumulative frequencies by keeping a running total of the frequencies.
Class Limits
Class Boundaries
Frequency
Cumulative Frequency 2 8 18 13 7 1 2 10 28 41 48 49 50
Bluman, Chapter 2

20. Excel tools Excel has a COUNTIF function.
See separate handout for details.
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21. Excel tools Excel has a FREQUENCY function
Put the raw data into some cells
Put the Upper Class Boundaries into some cells.
Array Formula =FREQUENCY(raw data, upper class boundaries) CTRL+SHIFT+ENTER
See separate handout for details.
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22. Excel tools In the Data Analysis tools, Histogram
As well as a histogram, it will set up classes and produce a frequency distribution
Details are in a separate handout in the Histogram lesson
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