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Frequency Tables Frequency Distributions Conclusion
MATH 105: Finite Mathematics 9-3: Organizing Data
- Prof. Jonathan Duncan
Frequency Tables Frequency Distributions Conclusion
MATH 105: Finite Mathematics 9-3: Organizing Data Prof. Jonathan - - PowerPoint PPT Presentation
MATH 105: Finite Mathematics 9-3: Organizing Data Prof. Jonathan - - PowerPoint PPT Presentation
Frequency Tables Frequency Distributions Conclusion MATH 105: Finite Mathematics 9-3: Organizing Data Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Frequency Tables Frequency Distributions Conclusion Outline Frequency
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Frequency Tables Frequency Distributions Conclusion
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
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Frequency Tables Frequency Distributions Conclusion
A Large Data Set
A typical larger data set may contain a wide range of data values and even have repeated values. It is often difficult to work with this raw data. Example The following is a list of scores made on a 60-point test. 25 30 34 37 41 42 46 49 53 26 31 34 37 41 42 46 50 53 28 31 35 37 41 43 47 51 54 29 32 36 38 41 44 48 52 54 30 33 36 39 41 44 48 52 55 30 33 37 40 42 45 48 52 Construct a frequency table for this data.
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Frequency Tables Frequency Distributions Conclusion
A Large Data Set
A typical larger data set may contain a wide range of data values and even have repeated values. It is often difficult to work with this raw data. Example The following is a list of scores made on a 60-point test. 25 30 34 37 41 42 46 49 53 26 31 34 37 41 42 46 50 53 28 31 35 37 41 43 47 51 54 29 32 36 38 41 44 48 52 54 30 33 36 39 41 44 48 52 55 30 33 37 40 42 45 48 52 Construct a frequency table for this data.
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Frequency Tables Frequency Distributions Conclusion
Frequency Table
Example Below is a frequency table for the data shown previously. Value Freq. Value Freq. Value Freq. 25 1 36 2 46 2 26 1 37 4 47 1 28 1 38 1 48 3 29 1 39 1 49 1 30 3 40 1 50 1 31 2 41 5 51 1 32 1 42 3 52 3 33 2 43 1 53 2 34 2 44 2 54 2 35 1 45 1 55 1
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Frequency Tables Frequency Distributions Conclusion
Line Chart
A frequency table can be represented graphically using a line chart.
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Frequency Tables Frequency Distributions Conclusion
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
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Frequency Tables Frequency Distributions Conclusion
Grouping The Data
Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution:
1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
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Frequency Tables Frequency Distributions Conclusion
Grouping The Data
Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution:
1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
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Frequency Tables Frequency Distributions Conclusion
Grouping The Data
Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution:
1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
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Frequency Tables Frequency Distributions Conclusion
Grouping The Data
Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution:
1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
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Frequency Tables Frequency Distributions Conclusion
Grouping The Data
Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution:
1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
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Frequency Tables Frequency Distributions Conclusion
Grouping The Data
Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution:
1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
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Frequency Tables Frequency Distributions Conclusion
Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
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Frequency Tables Frequency Distributions Conclusion
Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
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Frequency Tables Frequency Distributions Conclusion
Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 31-33.99 5 34-36.99 5 37-39.99 6 40-42.99 9 43-45.99 4 46-48.99 6 49-51.99 3 52-55 7 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
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Frequency Tables Frequency Distributions Conclusion
Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 31-33.99 5 34-36.99 5 37-39.99 6 40-42.99 9 43-45.99 4 46-48.99 6 49-51.99 3 52-55 7 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
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Frequency Tables Frequency Distributions Conclusion
Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 31-33.99 5 34-36.99 5 37-39.99 6 40-42.99 9 43-45.99 4 46-48.99 6 49-51.99 3 52-55 7 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
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Frequency Tables Frequency Distributions Conclusion
Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 31-33.99 5 34-36.99 5 37-39.99 6 40-42.99 9 43-45.99 4 46-48.99 6 49-51.99 3 52-55 7 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
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Frequency Tables Frequency Distributions Conclusion
A Histogram
The bar chart which is used with a frequency distribution is called a histogram. The line is called a frequency polynomial.
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Frequency Tables Frequency Distributions Conclusion
Another Frequency Distribution
What happens if we use the same data with a different number of classes? Example Construct a frequency distribution using a class width of 5. Question: Does changing the class width change the shape of the histogram?
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Frequency Tables Frequency Distributions Conclusion
Another Frequency Distribution
What happens if we use the same data with a different number of classes? Example Construct a frequency distribution using a class width of 5. Question: Does changing the class width change the shape of the histogram?
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Frequency Tables Frequency Distributions Conclusion
Another Frequency Distribution
What happens if we use the same data with a different number of classes? Example Construct a frequency distribution using a class width of 5. Class Interval Frequency 25-29.99 4 30-34.99 10 35-39.99 9 40-44.99 12 45-49.99 8 50-55 10 Question: Does changing the class width change the shape of the histogram?
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Frequency Tables Frequency Distributions Conclusion
Another Frequency Distribution
What happens if we use the same data with a different number of classes? Example Construct a frequency distribution using a class width of 5. Class Interval Frequency 25-29.99 4 30-34.99 10 35-39.99 9 40-44.99 12 45-49.99 8 50-55 10 Question: Does changing the class width change the shape of the histogram?
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Frequency Tables Frequency Distributions Conclusion
New Histogram
The smaller class width does produce a differently shaped histogram.
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Frequency Tables Frequency Distributions Conclusion
Compare Histograms
Compare the two histograms side-by-side to see this difference.
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Frequency Tables Frequency Distributions Conclusion
Compare Histograms
Compare the two histograms side-by-side to see this difference. Notice that the heights in the middle are more distinct in the left histogram than in the right histogram.
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Frequency Tables Frequency Distributions Conclusion
Frequency Tables vs. Frequency Distributions
There are both advantages and disadvantages to using a frequency distribution instead of a frequency table. Advantages of Frequency Tables
1 Individual data points are still visible. 2 Graph is not affected by choice of class width.
Advantages of Frequency Distributions
1 Individual data points are lost. 2 Changing class width can change shape of graph.
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Frequency Tables Frequency Distributions Conclusion
Frequency Tables vs. Frequency Distributions
There are both advantages and disadvantages to using a frequency distribution instead of a frequency table. Advantages of Frequency Tables
1 Individual data points are still visible. 2 Graph is not affected by choice of class width.
Advantages of Frequency Distributions
1 Individual data points are lost. 2 Changing class width can change shape of graph.
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Frequency Tables Frequency Distributions Conclusion
Frequency Tables vs. Frequency Distributions
There are both advantages and disadvantages to using a frequency distribution instead of a frequency table. Advantages of Frequency Tables
1 Individual data points are still visible. 2 Graph is not affected by choice of class width.
Advantages of Frequency Distributions
1 Individual data points are lost. 2 Changing class width can change shape of graph.
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Frequency Tables Frequency Distributions Conclusion
Cumulative Frequency Distributions
The last topic we will consider in this section is that of a cumulative frequency distribution. This is found by adding the number of data points in all previous classes together. Example Construct a cumulative frequency distribution using a class width
- f 5.
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Frequency Tables Frequency Distributions Conclusion
Cumulative Frequency Distributions
The last topic we will consider in this section is that of a cumulative frequency distribution. This is found by adding the number of data points in all previous classes together. Example Construct a cumulative frequency distribution using a class width
- f 5.
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Frequency Tables Frequency Distributions Conclusion
Cumulative Frequency Distributions
The last topic we will consider in this section is that of a cumulative frequency distribution. This is found by adding the number of data points in all previous classes together. Example Construct a cumulative frequency distribution using a class width
- f 5.
Class Interval Frequency Cumulative Freq. 25-29.99 4 4 30-34.99 10 14 35-39.99 9 23 40-44.99 12 35 45-49.99 8 43 50-55 10 53
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Frequency Tables Frequency Distributions Conclusion
Cumulative Frequency Polynomial
Below is the cumulative frequency polynomial for this data.
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Frequency Tables Frequency Distributions Conclusion
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
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Frequency Tables Frequency Distributions Conclusion
Important Concepts
Things to Remember from Section 8-2
1 Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
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Frequency Tables Frequency Distributions Conclusion
Important Concepts
Things to Remember from Section 8-2
1 Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
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Frequency Tables Frequency Distributions Conclusion
Important Concepts
Things to Remember from Section 8-2
1 Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
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Frequency Tables Frequency Distributions Conclusion
Important Concepts
Things to Remember from Section 8-2
1 Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
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Frequency Tables Frequency Distributions Conclusion
Next Time. . .
In the next section we will look at several different ways to compute the measure of the center of a data set. For next time Read section 9-4
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Frequency Tables Frequency Distributions Conclusion