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Frequency Distribution

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1 Frequency Distribution
A table with categories or classes and counts of how many data in each 11/30/2018

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 11/30/2018

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. 11/30/2018

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 11/30/2018

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 11/30/2018

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 11/30/2018

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 11/30/2018

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 11/30/2018

9 About the classes CLASS LIMITS are 10-19, 20-29, etc.
11/30/2018 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. < ) 11/30/2018

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. 11/30/2018

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 11/30/2018

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. 11/30/2018

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. 11/30/2018

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 11/30/2018


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