1. Complement Rule Mini-Quiz
Review
Complement Rule Mini-Quiz
An outbreak of food poisoning occurs in a group of students who attended a party
Sick
Not Sick
Total
Ate Barbecue
Did Not Eat Barbecue 90 20 30 60
120 80
110
200
(a) What is the complement of “Not Sick”?
(b) What is the probability of the complement?
(c) What is the complement of “Did Not Eat Barbecue”?
(d) What is the probability of the complement?

2. Class Greeting

3. Objective: The students will be able to make decisions by using statistical analysis.

4. Decision Making Using Statistical Analysis

6. Lesson 9 Ex2 Choose an Appropriate Measure
SURVEYS Eleanor took a poll in her class to see how many times her classmates had visited the local amusement park during summer vacation. What measure of central tendency best represents the data?
The data is: 5, 0, 2, 3, 2, 4, 1, 2, 1, 3, 8, 2, 2, 0.
Since there is an extreme value of 8, the median would best represent the data.
0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 8
Answer: The median is 2. This is also the mode.

7. BOWLING Jenny’s bowling scores are 146, 138, 140, 142, 139, 138, and 145. Which measure of central tendency best represents the data?
A. mean
B. median
C. mode
D. cannot be determined

8. Lesson 9 Ex3
QUIZ SCORES The quiz scores for students in a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Which measure of central tendency best represents the data? Then find the measure of central tendency.
The data value 0 appears to be an extreme value. So, the median and mode would best represent the data.
0, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10
Answer: The median and mode are 8.

9. Lesson 9 Ex3
Check You can check whether the median best represents the data by finding the mean with and without the extreme value.
mean with extreme value mean without extreme value
The mean without the extreme value is closer to the median. The extreme value decreases the mean by about 0.7. Therefore, the median best represents the data.

10. BIRTH WEIGHT The birth weights of ten newborn babies are given in pounds: 7.3, 8.4, 9.1, 7.9, 8.8, 6.5, 7.9, 4.1, 8.0, 7.5. Tell which measure of central tendency best represents the data. Then find the measure of central tendency.
A. mean, 7.53
B. median, 7.9
C. mode, 7.9
D. cannot be determined

11. Lesson 9 Ex4
SALARIES The monthly salaries for the employees at Bob’s Book Store are: $1290, $1400, $1400, $1600, $2650. Which measure of central tendency should Bob’s Book Store’s manager use to show new employees that the salaries are high?
A mode B median
C mean D cannot be determined
Read the Test Item
To find which measure of central tendency to use, find the mean, median, and mode of the data and select the greatest measure.

12. Lesson 9 Ex4 Solve the Test Item Mode: $1400
Median: $1290, $1400, $1400, $1600, $2650
Mode: $1400
Answer: The mean is the highest measure, so the answer is C.

13. EXERCISE The number of hours spent exercising each week by women are: 1, 6, 4, 2, 1, and 8. Which measure of central tendency should a person use to show that women do not spend enough time exercising?
A. mode
B. median
C. mean
D. cannot be determined

14. Extreme values and their effect on the mean
Here are some 1500 metre race results in minutes.
Are there any extreme values?
Will the mean be increased or reduced by the extreme value?
Calculate the mean with the extreme value.
Now calculate the mean without the extreme value. How much does it change?
The mean with the extreme value is 59.1 ÷ 9 = 6.57 minutes
The mean without the extreme value is ÷ 8 =6.06 minutes
Another example of when an extreme value would occur is an experiment on reaction time, where an anomalous result (e.g. if the participant’s hand slips) will be very large compared with the rest of the results.
What measure of the central tendency would be best to use?
It may be appropriate in research or experiments to remove an extreme value before carrying out analysis of results.

15. Standard Deviation
The math test scores of five students are: 92,88,80,68 and 52.
The square root of the variance is
Thus the standard deviation of the test scores is

16. Find the standard deviation.
Five different students took the same test with these test scores: 92,92,92,52,52.
Find the standard deviation.
The square root of the variance is
Thus the standard deviation of the second set of test scores is 19.6.

17. Analyzing the Data
Consider both sets of scores. Both classes have the same mean, 76. However, each class does not have the same scores. Thus we use the standard deviation to show the variation in the scores. With a standard variation of for the first class and 19.6 for the second class, what does this tell us?
A lower standard deviation means that the test scores will be close to each other.

18. Analyzing the Data Class A: 92,88,80,68,52 Class B: 92,92,92,52,52
With a standard variation of for the first class and 19.6 for the second class, the scores from the first class would be closer together than the scores in the first class.

19. Analyzing the Data Class B: 92,92,92,52,52
Class A: 92,88,80,68,52
Class B: 92,92,92,52,52
Class C:77,76,76,76,75
Estimate the standard deviation for Class C.
a) Standard deviation will be less than
b) Standard deviation will be greater than 19.6.
c) Standard deviation will be between and 19.6.
d) Can not make an estimate of the standard deviation.

20. Answer: A Analyzing the Data
Class A: 92,88,80,68,52
Class B: 92,92,92,52,52
Class C: 77,76,76,76,75
Estimate the standard deviation for Class C.
a) Standard deviation will be less than
b) Standard deviation will be greater than 19.6.
c) Standard deviation will be between and 19.6
d) Can not make an estimate if the standard deviation.
Answer: A
The scores in class C have the same mean of 76 as the other two classes. However, the scores in Class C are all much closer to the mean than the other classes so the standard deviation will be smaller than for the other classes.

21. Analyzing the Data Class B: 92,92,92,52,52 Class C: 77,76,76,76,75
Class A: 92,88,80,68,52
Class B: 92,92,92,52,52
Class C: 77,76,76,76,75
Estimate the standard deviation for Class C.
a) Standard deviation will be less than
b) Standard deviation will be greater than 19.6.
c) Standard deviation will be between and 19.6
d) Can not make an estimate if the standard deviation.

22. Recap:
As we have seen, standard deviation measures the dispersion of data.
The greater the value of the standard deviation, the further the data tend to be dispersed from the mean.

23. Lesson Summary:
Objective: The students will be able to make decisions by using statistical analysis.

24. Objective: The students will take a practice test on statistics.
Preview of the Next Lesson:
Objective: The students will take a practice test on statistics.

25. Homework
Statistics HW 14 and HW 7