1. Unit Activation M & M distribution project
How are probability and statistics related?

2. Statistics
How can we represent a set of data so that it has meaning to those who need to view it?

3. How do statistics help me relate to the world around me?
Statistics Review 16-1 & 2
How do statistics help me relate to the world around me?

4. A Statistics Review Game
Greed
A Statistics Review Game

5. Set up your sticky note like this with the sticky part on top
Round Score
1 _____
2 _____
3 _____
4 _____
5 _____
total

6. Instructions 1) Everyone begins the game by standing
2) Two six-sided die are rolled for the initial score
3) Those that are happy with their score may sit down and record their score on Their Sticky note
4) The round ends when a one is rolled or everyone sits down. If a one is rolled everyone standing gets a zero for the round
5) A game consists of 5 rounds
6) At the end of five rounds, students add their scores together
7) The data is then used to review statistics concepts

7. Roll two six-sided dice for the initial score
Click to Roll

8. Repeat until a one is rolled.
Roll one six sided die
Repeat until a one is rolled.
Play 5 rounds
Click to roll

9. Calculate your score
Round Score 1 2 3 4 5
total

10. Place the papers on the board in numeric order
FIND THE:
Mean
Median
Mode
Create a Box and Whisker Plot
Discuss outliers (not just extremes)
Create a dot plot
Create a stem plot
State the similarities and differences between dot and stem plots
Play round two

11. Set up your sticky note like this with the sticky part on top
Round Score 1 2 3 4 5
total

12. Roll two six-sided dice for the initial score
Click to Roll

13. Repeat until a one is rolled.
Roll one six sided die
Repeat until a one is rolled.
Play 5 rounds
Click to roll

14. Calculate your score
Round Score 1 2 3 4 5
total

15. Place the papers on the board in numeric order
Create a back to back stem plot
Compare and Contrast the two stem plots (Center, Shape and Spread—range)

16. NONE.
Homework

17. How do I interpret graphs and charts?
Chapter 16-2a
How do I interpret graphs and charts?

18. Statistics in the World
How many sectors are in this circle graph? 5
What percentage of people in Shrub Oak preferred chocolate ice cream? 35
What percentage of people in Shrub Oak preferred butter pecan ice cream? 13
If a total of 50 people were surveyed, then how many people preferred vanilla ice cream? 13

19. Not given
0 to 100 6
Visit with friends
School clubs 53 44
Watch TV and earn money
Visit w friends, chat online, talk on phone, earn money, watch tv, school clubs

20. Choice 3

21. Discuss this as a class

22. What is wrong with the graph?
a) the labels are missing
b) scale is incorrect
c) too much data is presented for this type of graph
d) none of the above

23. How can we represent this data?
what type of graphs do you think is best for this data and why?
One option is to the right,
Is this the only option?
No you could use a bar graph too

24. WORKSHEET Graphs
Homework

25. How to we find the measures of variation and what do they mean?
Chapter 16-3
How to we find the measures of variation and what do they mean?

26. definitions
Mean deviation—the average distance each piece of data is from the mean
Variance—the measure of the amount of variation in a set of data
Standard deviation—the square root of the variance or the typical deviation from the mean in normal data all data should fall within three SD of the mean

27. Example
20, 15, 12, 18, 17, 15, 17, 16, 18, 25
Reorder
12, 15, 15, 16, 17, 17, 18, , 25
range =
iqr =
173
=17.3 10
Median= 17
Q1= 15
Q3= 18
25-12=13
18-15=3

28. Just Watch!!!!!!!!! Find the standard deviation by hand i xi Xi- 1 1215 3 4 16 5 17 6 7 18 8 9 20 10 25
totals
Xi-
-5.3
-2.3
-1.3
-.3 .7
2.7
7.7
(xi- )2
28.09
5.29
1.69
.09
.49
7.29
59.29
108.1
173

29. By Calculator Press Stat Press STAT Press enter/edit
Enter the data in L1
Press STAT
Choose calc
Choose 1 var stat xi 12 15 16 17 18 20 25

30. Finding the Mean Deviation with the Calc
Enter the data in L1
Go to the top of L2 and enter |xi - 𝑥 |
Run 1 variable statistics on L2
The 𝑥 in this run is the mean deviation

31. Pg. 702
2, 4, 6, 7
Homework

32. The Normal Distribution 16-4

33. Activation
Roll two die 5 times recording your results. Take turns plotting the results on the graph below. 2 3 4 5 6 7 8 9 10 11 12

34. The normal curve
Normally Distributed data—data which is bell shaped and symmetric about the mean in a way that 68% of the data fall within one st. dev., 95% fall within two st. dev. And 99.7% falls within 3 standard dev.
mean
68%
13.5%
2.35%
95%
99.7%

35. Z-scores
Z-score—the number of standard deviations a piece of data falls from the mean
Example: if the mean is 10 and the st dev is 2
What is the z-score of 7
Open the book to pg 850.

36. What does a z-score mean?
Z-chart—because the data is symmetric we can find the likelihood that we will have this piece of data or one less than it.
6.68% of the data is less than or equal to 7 when the mean is 10 and the st dev is 2

37. Example
Samples of a certain type of concrete specimen are selected, and the compressive strength of each one is determined. The mean and st. dev are and 500 respectively. The sample box-plot appears relatively normal. (i.e.—we can use z-scores)
Approx. what % of the sample falls below 2500?
Approx what percent falls between 2500 and 4300?
Approx what percent falls above 4500?

38. Pg 708
15-18
Homework

39. 16-5
Sampling

40. Simple Random Sample—samples chosen so that
Each item has an equal chance of being selected
The choice of one item has no bearing on the choice of the next
Example:
A scientist is testing the impact on weight gain and loss on rats fed a certain supplement. He reaches into the cage and chooses the five largest rats. Is this a random sample?
This is not random in fact it is what we call biased.

41. Bias—when data is overly influenced for some reason.
In the last example the scientist was biased towards the larger rats.
Examples:
The county decides to survey the size of its constituents households by calling every 10th person on the list?
Is this random?
Yes –not necessarily the best way to achieve randomness but legitimate
Is this biased?
Yes—not all constituents may have a home phone

42. Closer—Happyville Keep the worksheet face down until told differently
When I tell you turn the worksheet over and estimate the average household size in Happyville—you have five seconds turn the paper back
Get everyone’s values and find the average of the estimates
When I tell you turn the paper over and randomly choose any ten households by circling them (you have 30 seconds)—turn the paper back
Average the number of people in the 10 households
Get everyone’s values and find the average of the averages
Compare the two values
Seed the random number generator
Type in a value from 0 to 1000 press STO math prb rnd
Then type math prb 5 (1,100) press enter until you have 10 unique values
Average the number of people in these 10 households
Compare the three values
Which values are closest together?

43. Pg 713
evens
Homework

44. Simulations 16-7

45. Activation
What is the probability of getting 5 heads when you flip a coin ten times? Is it sufficient to flip the coin just ten times? Ten sets of ten? What if the experiment had been what is the probability of getting 5 correct answers on a ten problem true false test?

46. Simulations Theoretical probability Experimental probability
The actual probability of an event
Experimental probability
The results that you get when you run an experiment
Simulation
Used to approximate the probability when money or time is too great a factor in running an actual experiment
Design
The method used to run the simulation
Trial
One run of the method described

47. Example one:
A restaurant is giving away 6 actions figures to the latest movie with the purchase of each child’s meal. If you are equally like to get any figure, what is the probability of getting one of each in the purchase of ten meals?
Click to roll

48. Example Two:
A basketball player has a free throw percentage of 80%. What is the probability of making two free throws out of three baskets?

49. Example Three: How does this change our simulation?
A basketball player has a free throw percentage of 78%. What is the probability of making two free throws in a out of three?

50. Worksheet
Homework

51. Is one type of sampling better than another?
Types of sampling 16-6
Is one type of sampling better than another?

52. What are the types of sampling and how is each accomplished?
River Project
What are the types of sampling and how is each accomplished?

53. Harvest Time
A farmer has just cleared a new field for corn. It is a unique plot of land in that a river runs along one side. The corn looks good in some areas of the field but not others. The farmer is not sure that harvesting the field is worth the expense. He has decided to harvest 10 plots and use this information to estimate the total yield. Based on this estimate, he will decide whether to harvest the remaining plots.

54. Convenience Sample
The farmer decided to harvest the 10 easiest plots to harvest. He then had second thoughts and decided to hire you, a statistics student, somewhat knowledgeable about these matters but far cheaper than a statistician. You are still to choose 10 plots but try different sampling methods to determine which one will give the best estimate of the actual yield. X
River

55. Simple Random Sample
Use a random number table to select 10 plots. Describe the method used and mark the plots.
River

56. Stratified Sample (vertical)
Determine a method that will allow you to choose one box in each column. Describe the method and select the plots
River

57. Stratified Sample (horizontal)
Determine a method that will allow you to choose one box in each row. Describe the method and select the plots
River

58. Determining best method
The table below represents the yield per plot. You will need this to determine which method is best and why. 1 2 3 4 5 6 7 8 9

59. Determining best method
Mean yield
per plot
Estimated
Total yield
Convenience sample
Simple Random sample
Vertical strata
Horizontal strata

60. Observations
You looked at four different methods of choosing plots. Is there a reason, other than convenience, to choose one method over another?
How did your estimates vary according to the different sampling methods used?

61. None
Homework

62. How much of a difference is enough?
Hypothesis testing
How much of a difference is enough?

63. Distracted Driver Project

69. 1. Get a standard deck of 52 cards (i.e. no jokers)
2. Work with your group to determine a method for simulating this experiment using the cards. Take five minutes to determine your method.
We will discuss the methods before proceeding and all use the same method.
Shuffle and deal two piles of 24 cards. The pile on the left will be the cell-phone drivers. Record the number who missed. Why don’t we need to count the cards in the other pile?

70. 5. Make a chart like the one below and repeat the experiment 9 more times recording the number of cell phone misses.
6. In the original experiment, 7 of 24 drivers using cell phones missed the freeway exit, compared to only 2 of the 24 drivers talking to a passenger. In how many of your 10 simulation trials did 7 or more drivers in the cell phone group miss the exit?

71. Place your results in the class dot plot on the board
Place your results in the class dot plot on the board. In what percent of the class’s simulation trials did 7 or more people in the cell phone group miss the freeway? (be careful to keep the rows and columns of dots even)
8. Since 7 of the cell phone talkers missed the exit in the actual experiment, do you think it’s possible that cell phones and passengers are equally distracting to drivers based on the simulation results of the class? Why or why not?

73. None
Homework