1. Introduction
In a survey of 100,000 women conducted in the mid 1980’s, it was found that over 70% of women who were married for more than five years had had an affair.
What do you think?

2. Things to consider when looking at data…
Who conducted the study?
What did the sample look like?
Were the people surveyed those who had biases?
Was the sample representative of the actual population?

3. What about this?
There was a larger survey done of 200,000 women and they reported 15% of women had been unfaithful.
What does this mean?
Which survey should be believed?

4. 14.1 Organizing & Visualizing Data
Probability and Statistics
Ms. DiMarzio

5. We are going to study Statistics – area of math in which we are interested in gathering, organizing, analyzing and making predictions from data.
Data: numerical information.

6. What is the difference between a sample and population?
A Population is everyone/everything being considered.
For example: In the survey on married women, the population is all married women.
Not always realistic to get all of the population surveyed.
A Sample is a part of a population.
This is more realistic in some situations to use.
The sample should be typical of the population as a whole.

7. Biased a sample is biased if it does not accurately reflect the population as a whole with regard to the data we are gathering. Bias often happens if we use poor sampling techniques.
2 types of bias:
Selection bias. This is the way we choose who will be in our sample.
Example 1: A phone survey on a Wednesday afternoon. Who will be home?
Example 2: Call in surveys to news shows or radio stations.
Leading question bias: The way we ask a question.
Example: Will you support Mayor Smith after his recent arrest?

8. Homework :
14.1 Examples worksheet

9. Notes Part 2

10. ORGANIZING DATA

11. What do you do with the data you collect?
You need to organize it in a meaningful way to it is possible to interpret facts.
You need to organize it and present it so you can see patterns, trends and relationships.
How do we do this?
LOOK AT FREQUENCY – how many times something happens …
Or RELATIVE FREQUENCY – what percent of the time something happens

12. A frequency distribution is a collection of numerical information.
Example : Grade Frequency A B C D E
Relative Frequency: Percent of the time each item occurs in a frequency distribution. This is a better way to compare sets of data.
Example:
Grade Frequency Relative Frequency
A 6 6/10 = .60 = 60%
B 1 1/10 = .10 = 10%
C 0 0/10 = 0%
D 1 1/10 = .10 = 10%
E 2 2/10 = .20 = 20%

13. FOR YOU TO TRY:
Construct a table showing frequency and relative frequency for the following high temperatures for the last 2 weeks of August:
80, 96, 75, 70, 92, 96, 83, 75, 80, 83, 95, 96, 80, 72

14. August Temperatures Temperature Frequency Relative Frequency 70 1
1/14 = .071= 7.1% 72 75 2
2/14 = .142 = 14.2% 80 3
3/14 = .21 4= 21.4% 83 92 95 96
3/14 = .214 = 21.4%

15. Bar Graphs: One visual way to represent data.
A good way to represent frequency data
It must have a title
x and y axis labeled
Bars neatly made and space in between (not connected)

16. Histogram: A special type of bar graph that is used when there are continuous variables (DECIMALS) , or RANGES
It must have a title
x and y axis labeled
Intervals equal
Bars neatly made and
no space in between
(connected)

17. Which type of graph to use?
Bar graph: frequency information
Histogram: decimals or ranges

18. Example: Grades on quizzes
Stem and Leaf: an effective way to present two sets of data side by side for analysis
Example: Grades on quizzes
1st hour: 51, 55, 75, 77, 78, 78, 79, 80, 82, 85, 85, 86, 87, 88, 89, 93, 93, 96, 100, 100
5th hour: 40, 61, 62, 68, 70, 75, 75, 78, 78, 85, 85, 85, 88, 88, 88, 89, 90, 91, 95, 99, 100
1st Hour
Stem
5th Hour 4
5,1 5 6
1,2,8
9,8,8,7,5 7
0,5,5,8,8
9,8,7,6,5,5,2,0 8
5,5,5,8,8,8,9
6,3,3 9
0,1,5,9
0,0 10

19. Example 1 – construct frequency table, relative frequency table, bar graph
11, 15, 15, 10, 11, 9, 15, 11, 13, 9

20. Example 2 – construct bar graph for relative frequency
Number
Frequency
Relative Frequency 9 2
2/10 = 0.20 or 20% 10 1
1/10 = 0.10 or 10% 11 3
3/10 = 0.30 or 30% 12 0% 13 14 15

21. Example 3 – construct histogram for weight gain of 10 people
Example 3 – construct histogram for weight gain of 10 people. Use a ‘class width’ (range) of 2, starting at 0
1.5, 0, 5, 6.2, 2.3, 8.7, 6.1, 0, 2.2, 5.4

22. Example 4 – interpret a bar graph with frequency
Which color/colors were least favorite?
How many people were surveyed?
How many people liked red or green?

23. HOMEWORK ASSIGNMENT:
p. 789 # 1-9, 12 ,14, 18, 24