1. The Frequency Distribution
Statistics
The Frequency Distribution

2. Essential Question
What are some different ways that numerical data can be represented?

3. Univariate Data Single variable data
Basic statistical data which can’t be influence by another variable

4. Frequency Distribution
4 Main Ways
Bar Graph
Frequency Distribution
Histogram
Frequency Polygon

5. Bar Graphs
Bar graphs are good for a variety of data including categories and numerical data
Bar graphs are also good if you are wanted to compare data with either a back to back bar graph or side to side bar graph

6. Bar Graphs continued:
In 1973 the music industry sold the following quantities: 280 million albums, 228 million 45’s, 15 million cassette tapes and 0 CD’s
How would you represent this data in a bar graph?

7. Bar Graphs continued:
In 1990 the music industry sold the following quantities: 12 million albums, 28 million 45’s, 442 million cassette tapes and 287 CD’s
How would you compare this data to the previous data?
How might this graph look different today?

8. Bar Graphs continued:

9. Frequency Distribution
Used when lots of numerical data needs to be grouped together
Method for organizing data based on quantity

10. Frequency Distribution
Divides the numbers into classes of equal value:
5 – 10
10 – 15
Class Interval
Range: UL – LL
All range values are the same
Class Mark: (UL + LL)/2
The Class Mark is the middle of each class – find each
Upper Limit
Lower Limit

11. Example of a Frequency Distribution:
Tree Diameter (in)
Frequency
0 – 2 6
2 – 4 30
4 – 6 38
6 – 8 33
8 – 10 4
Frequency can be zero
Includes trees 10 inches wide up to but not including 12 inches

12. Making a Frequency Distribution
Find the range of values for the data set (highest number – lowest number)
Divide the range by the number of classes you want (for small sets of data lets say 5 or 6) – this is the class range
Create your classes by adding the class range to the lowest number (or something smaller)
Continue until you reach a number bigger than your largest numer
Tally up the numbers in each class

13. Now lets try (Scores on a Test)95 52 72 85 89 78 65 77 70 82 75 96 35 88 92 81 30 55 76 83 61 68 73 99 74 54 91 67 71 80

14. Histogram
Bar graph in which the width of each bar represents a class interval and the height represents the frequency of the data (must be numerical in value.
Different with bar graph ….

15. Example of a Histogram:
Tree Diameter (in)
Frequency
0 – 2 6
2 – 4 30
4 – 6 38
6 – 8 33
8 – 10 4

16. Create your own Histogram:
“26-32” represents a__
What are the class marks?
What is the class interval?
The limits of the class are
What percent earned between $38,000 and $44,000?
What percent earned at least $38,000?
Salary (Thousands of dollars
Frequency
20 – 26 6
26 – 32 30
32 – 38 38
38 – 44 33
44 – 50

17. Frequency Polygon:
Broken line graph created by connecting the class marks of each bar on a histogram

18. Example of a Frequency Polygon:
Tree Diameter (in)
Frequency
0 – 2 6
2 – 4 30
4 – 6 38
6 – 8 33
8 – 10 4

19. Add a Frequency Polygon to your created histogram:
Salary (Thousands of dollars)
Frequency
20 – 26 6
26 – 32 30
32 – 38 38
38 – 44 33
44 – 50 13

20. Cumulative Frequency
The total of your frequency

21. Univariate Data (Day 1) Make a frequency Distribution
Create a histogram graph
Create a frequency polygon graph

23. True or False?
A class interval is the same as the range of each class.
A frequency distribution shows individual pieces of data
A frequency distribution shows the comparison of two sets of data
Class intervals are represented by the width of each bar in a histogram
Each Class should have different range
If a class has limits of 17 and 24 its class mark is 21.5.

24. Revisiting the EQ:
What are some different ways that numerical data can be represented?