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Frequency Distribution
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A frequency distribution is a is a grouping of
data into mutually exclusive categories showingthe number of observations in each class..
Two types frequency distributions are:1. Numerical
Frequency distribution that has quantitative group
in each class.
2. CategoricalFrequency distribution that has qualitative groupin each class.
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Determining the question to be addressed
Constructing frequency distribution is a part in describedatas the we collect.
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Determining the question to be addressed
Collecting raw data
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Determining the question to be addressed
Collecting raw data
Organizing data (frequency distribution)
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Determining the question to be addressed
Collecting raw data
Organizing data (frequency distribution)
Presenting data (graph)
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Determining the question to be addressed
Collecting raw data
Organizing data (frequency distribution)
Presenting data (graph)
Drawing conclusions
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Terminologies in Frequency Distribution
Class Limit : Numbers that separate between twoclasses. Two kinds are lower class and upper class.
Class Frequency : The number ofobservations in each class.
Class Boundary : A midpoint between alower class limit and upper class limit forthe previous class.
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Weekly Earnings Number of
Employees, f
301 400 9401 500 16501 600 33601 700 20
701 800 14
801 900 8
Total number of employees 100
Fifth class
Lower limit ofthe sixth class
Upper limit ofthe sixth class
Frequency ofthe third class
Classboundary ?
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Class Midpoint : A point that divides a class intotwo equal parts. This is the average of the upperand lower class limits.
Open Class : Classthat have no upper
limit.
Class interval : The classinterval is obtained bysubtracting the lower limit ofa class from the lower limit ofthe next class. The classintervals should be equal.
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Weekly Earnings Number ofEmployees
301 400 9401 500 16501 600 33
601 700 20
701 800 14
801 900 8
Total number of employees 100
Midpoint is (301+400)/2 = 350,5
Class Interval is?
Class Interval is?
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A Relative Frequency Distribution shows the percent ofobservations in each class.
Cumulative Frequency Distribution is used todetermine how many or what proportion of the data
values are below or above a certain value.
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WeeklyEarnings
Number ofEmployees Relative
frequencyCommulativefrequency
301 400 9 9/100 9
401 500 16 16/100 25
501
600 33 33/100 58601 700 20 20/100 78
701 800 14 14/100 92
801 900 8 8/100 100
Total number ofemployees
100 1
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The three commonly used graphic forms areHistograms, Polygons , and a Cumulative
Frequency distribution.
A Histogram is a graph in which the class midpoints orlimits are marked on the horizontal axis and the classfrequencies on the vertical axis.The class frequencies are represented by the heights of thebars and the bars are drawn adjacent to each other.
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A Frequency Polygon consists of line segmentsconnecting the points formed by the class midpoint
and the class frequency.
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Construct frequency distribution
1. Sort raw data in ascending order2. Decide on the number of classes using the formula
k = 1 + 3,322 log n
where k=number of classes
n=number of observations3. Determine the class interval or width using the
formula
4. Set the individual class limits
5. Tally and count the number of items in each class.
H Lk
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6. Construct the frequency distribution and complete withclass midpoint, relative frequency, and CumulativeFrequency
Example: A manufacturer of winter coatrandomly selects 20 winter days andrecords the daily temperature.
24, 35, 17, 21, 24, 37, 26, 46, 58, 30,
32, 13, 12, 38, 41, 43, 44, 27, 53, 27
1. Sort raw data in ascending order:
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2. Class number : 3. Class interval :
4. Set the individual class limit and construct thefrequency distribution
Interval Tally Fi Midpoint
Total 20 20 1
RelativeFrequency
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IntervalCumulative
Frequency Cumulative
Frequency Frequency
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Histogram: Daily High Temperature
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