MATH 105: Finite Mathematics 9-3: Organizing Data
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1 MATH 105: Finite Mathematics 9-3: Organizing Data Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006
2 Outline 1 Frequency Tables 2 Frequency Distributions 3 Conclusion
3 Outline 1 Frequency Tables 2 Frequency Distributions 3 Conclusion
4 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 Construct a frequency table for this data.
5 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 Construct a frequency table for this data.
6 Frequency Table Example Below is a frequency table for the data shown previously. Value Freq. Value Freq. Value Freq
7 Line Chart A frequency table can be represented graphically using a line chart.
8 Outline 1 Frequency Tables 2 Frequency Distributions 3 Conclusion
9 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
10 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
11 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
12 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
13 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
14 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
15 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
16 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
17 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 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper lower 2
18 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 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper lower 2
19 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 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper lower 2
20 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 Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper lower 2
21 A Histogram The bar chart which is used with a frequency distribution is called a histogram. The line is called a frequency polynomial.
22 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?
23 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?
24 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 Question: Does changing the class width change the shape of the histogram?
25 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 Question: Does changing the class width change the shape of the histogram?
26 New Histogram The smaller class width does produce a differently shaped histogram.
27 Compare Histograms Compare the two histograms side-by-side to see this difference.
28 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.
29 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.
30 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.
31 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.
32 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 of 5.
33 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 of 5.
34 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 of 5. Class Interval Frequency Cumulative Freq
35 Cumulative Frequency Polynomial Below is the cumulative frequency polynomial for this data.
36 Outline 1 Frequency Tables 2 Frequency Distributions 3 Conclusion
37 Important Concepts Things to Remember from Section Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
38 Important Concepts Things to Remember from Section Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
39 Important Concepts Things to Remember from Section Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
40 Important Concepts Things to Remember from Section Constructing Frequency Distributions 2 Constructing Histograms 3 Cumulative Frequency Distribution
41 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
42 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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