1. Read page 41
Do the Academy Awards involve discrimination based on age?
What do you think?

2. Summarizing and Graphing Data
Identify five important characteristics of data. Construct a frequency distribution, identify the class width, class midpoints, and the class boundaries.

3. Organizing, summarizing, and graphing sets of data.
Ultimate Objective: UNDERSTAND TO DATA
Important Characteristics of Data:
Center
Indicates the middle of the data set
Variation
Measures the amount that the data values vary among themselves
Distribution
Nature of shape of the distribution (normal “bell”, uniform, skewed)
Outliers
Sample values that lie very far away from the vast majority of the other sample values
Time
Changing characteristics of data over time

4. Computer Viruses Destroy Or Terminate
As proceed through class, we will be performing a few manual calculations but the focus will be on obtaining results by using some form of technology.

5. Frequency Distribution
Method of organizing large data sets
Helps statistician to understand the nature of the distribution of a data set.
Lists data values (either individually or by groups of intervals), along with their corresponding frequencies (or counts).

6. Look at table 2-2 on page 43 Frequency Distribution: Ages of Best Actresses
Lower Class Limits:
smallest numbers that belong to the different classes.
Upper Class Limits:
largest numbers that belong to the different classes.
Class Boundaries:
Numbers used to separate classes, but without gaps created by the class limits
Class Midpoints:
Values in the middle of the classes. Each class midpoint can be found by adding the lower class limit to the upper class limit and dividing the sum by 2
Class Width:
Difference between two consecutive lower class limits or consecutive lower class boundaries
Age of Actress
Frequency
21-30 28
31-40 30
41-50 12
51-60 2
61-70
71-80
Lower class limits: 21, 31, 41, 51, 61, 71
Upper class limits: 30, 40, 50, 61, 70, 80
Class boundaries: 20.5, 30.5, 40.5, 50.5, 60.5, 70.5, 80.5
Class midpoints: 25.5, 35.5, 45.5, 55.5, 65.5, 75.5
Class with: 10

7. Be careful to avoid the mistake of making the class width the difference between the lower class limit and the upper class limit.
Find class boundaries and find difference between class boundaries.

8. Constructing a Frequency Distribution
Constructed for Three Reasons
Large data sets can be summarized
Gain some insight into the nature of the data
Have a basis for constructing important graphs

9. Basic Procedure of Construction
1. Decide on the number of classes you want (should be between 5 and 20).
2. Calculate the class width (round to a convenient number.
[Maximum value – Minimum value]
number of classes
3. Find your starting point
(minimum value or a convenient # below it)
4. Using the lower limit of the first class and the class width, proceed to list the other lower class limits. (Add the class width to the starting point to get the second lower class limit.)

10. 5. List the lower class limits in a vertical column and proceed to enter the upper class limits.
6. Mark a tally in the appropriate class for each data value. Use the tally marks to find the total frequency for each class.
Construct a frequency distribution for the best actors from the list on page 41 as a class. Follow the six steps.
Number of classes, class width, starting point, lower limits, upper limits, tallies

11. Relative Frequency Distribution
Includes same class limits but shows percentages rather than actual frequencies.
Relative frequency: class frequency____
sum of all frequencies
Find the relative frequency distribution for the best actors.

12. Cumulative Frequency Distributions
Cumulative frequency is the sum of the frequencies of that class and all values below that class.
Shows number at or below
Find the cumulative frequency distributions for the best actor awards

13. Interpreting Frequency Distributions
Important objective: to identify the nature of the distribution
Normal (Bell) Shape Distribution:
Uniform Distribution:
Skewed Distribution

14. Look at table 2-5 on page 47. What type of distribution is this?
What kind of distribution is the best actor frequency distribution?

15. Identifying other information from frequency distributions.
Look at the frequency distributions on page 47
Look at the heart beat frequency table. Do you notice anything about the values?
Pulses counted for 15 seconds and multiplied by 4
Penny frequency distribution – what could the gaps mean?
Pennies from two populations; before 1983 and those after 1983
Can you recognize about actresses and actors from the frequency table?
Actresses tend to be younger than actors.

16. Assignment
Page 48 #1-14 all, 20, 22, 24