Frequency Tables
Frequency Distributions
MATH 105: Finite Mathematics
9-3: Organizing Data
Prof. Jonathan Duncan
Walla Walla College
Winter Quarter, 2006
Conclusion
Frequency Tables
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
Frequency Distributions
Conclusion
Frequency Tables
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
Frequency Distributions
Conclusion
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
26
28
29
30
30
30
31
31
32
33
33
34
34
35
36
36
37
37
37
37
38
39
40
41
41
41
41
41
42
42
42
43
44
44
45
Construct a frequency table for this data.
46
46
47
48
48
48
49
50
51
52
52
52
53
53
54
54
55
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
26
28
29
30
30
30
31
31
32
33
33
34
34
35
36
36
37
37
37
37
38
39
40
41
41
41
41
41
42
42
42
43
44
44
45
Construct a frequency table for this data.
46
46
47
48
48
48
49
50
51
52
52
52
53
53
54
54
55
Frequency Tables
Frequency Distributions
Conclusion
Frequency Table
Example
Below is a frequency table for the data shown previously.
Value
25
26
28
29
30
31
32
33
34
35
Freq.
1
1
1
1
3
2
1
2
2
1
Value
36
37
38
39
40
41
42
43
44
45
Freq.
2
4
1
1
1
5
3
1
2
1
Value
46
47
48
49
50
51
52
53
54
55
Freq.
2
1
3
1
1
1
3
2
2
1
Frequency Tables
Frequency Distributions
Conclusion
Line Chart
A frequency table can be represented graphically using a line chart.
Frequency Tables
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
Frequency Distributions
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
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
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
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
25-27.99
28-30.99
31-33.99
34-36.99
37-39.99
40-42.99
43-45.99
46-48.99
49-51.99
52-55
Frequency
2
5
5
5
6
9
4
6
3
7
Lower Class Limits:
The first number in the range.
Upper Class Limits:
The second number in the range.
Class Midpoint
upper − lower
2
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
25-27.99
28-30.99
31-33.99
34-36.99
37-39.99
40-42.99
43-45.99
46-48.99
49-51.99
52-55
Frequency
2
5
5
5
6
9
4
6
3
7
Lower Class Limits:
The first number in the range.
Upper Class Limits:
The second number in the range.
Class Midpoint
upper − lower
2
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
25-27.99
28-30.99
31-33.99
34-36.99
37-39.99
40-42.99
43-45.99
46-48.99
49-51.99
52-55
Frequency
2
5
5
5
6
9
4
6
3
7
Lower Class Limits:
The first number in the range.
Upper Class Limits:
The second number in the range.
Class Midpoint
upper − lower
2
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
25-27.99
28-30.99
31-33.99
34-36.99
37-39.99
40-42.99
43-45.99
46-48.99
49-51.99
52-55
Frequency
2
5
5
5
6
9
4
6
3
7
Lower Class Limits:
The first number in the range.
Upper Class Limits:
The second number in the range.
Class Midpoint
upper − lower
2
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.
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?
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?
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
25-29.99
30-34.99
35-39.99
40-44.99
45-49.99
50-55
Frequency
4
10
9
12
8
10
Question:
Does changing the class width
change the shape of the histogram?
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
25-29.99
30-34.99
35-39.99
40-44.99
45-49.99
50-55
Frequency
4
10
9
12
8
10
Question:
Does changing the class width
change the shape of the histogram?
Frequency Tables
Frequency Distributions
New Histogram
The smaller class width does produce a differently shaped
histogram.
Conclusion
Frequency Tables
Frequency Distributions
Compare Histograms
Compare the two histograms side-by-side to see this difference.
Conclusion
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.
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.
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.
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.
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
of 5.
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
of 5.
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
of 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
8
43
45-49.99
50-55
10
53
Frequency Tables
Frequency Distributions
Cumulative Frequency Polynomial
Below is the cumulative frequency polynomial for this data.
Conclusion
Frequency Tables
Outline
1
Frequency Tables
2
Frequency Distributions
3
Conclusion
Frequency Distributions
Conclusion
Frequency Tables
Frequency Distributions
Important Concepts
Things to Remember from Section 8-2
1
Constructing Frequency Distributions
2
Constructing Histograms
3
Cumulative Frequency Distribution
Conclusion
Frequency Tables
Frequency Distributions
Important Concepts
Things to Remember from Section 8-2
1
Constructing Frequency Distributions
2
Constructing Histograms
3
Cumulative Frequency Distribution
Conclusion
Frequency Tables
Frequency Distributions
Important Concepts
Things to Remember from Section 8-2
1
Constructing Frequency Distributions
2
Constructing Histograms
3
Cumulative Frequency Distribution
Conclusion
Frequency Tables
Frequency Distributions
Important Concepts
Things to Remember from Section 8-2
1
Constructing Frequency Distributions
2
Constructing Histograms
3
Cumulative Frequency Distribution
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion
Frequency Tables
Frequency Distributions
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
Conclusion