1. 8th Grade Chapter 12 Data Analysis and Probability

2. Frequency Table and Line plots 4/19
Range
Difference between the largest and smallest values in a data set
Lists each data item with the number of times it occurred
Frequency
Table
Example
Display the set of data in a frequency table:
Number 1 2 3 4
Frequency

3. Make a frequency table for the ages of students in this classroom.
1. Determine the range of ages of so you know what ages to list on the table
Age
Frequency
2. Gather data to determine the frequency of each age.

4. Displays data with an X mark above a number line
Line Plots
Displays data with an X mark above a number line
Write your favorite number (between 0 and 10) on the scrap of paper given to you
When your number is called come up to the board and place an x above your number—if there is already an x above your number, then put your x above that x

5. Use the information from the line plot you make a frequency chart on your own paper
Can you think of other data that could be arrange in a frequency chart or line plot?
Workbook
Page
You try

6. Box-and-Whisker Plots 4/20
15, 18, 21, 7, 29, 20, 9, 23, 25, 25, 29, 14, 8, 18, 26, 28, 27, 19, 7, 26
Write the numbers in order from least to greatest
Identify the smallest number
Identify the biggest number
Find the median (the middle number when the numbers are in order—if 2 numbers are in the middle, average them)
Find the range
Review

7. 7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29
20.5
Median
Data set

8. Find the median for the first half of the data
Divide the data into quartiles
7, 7, 8, 9, 14, 15, 18, 18, 19, 20
Median of 1st half: 14.5
7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29
14.5
Median
1st half
20.5
Median
Data set

9. Find the median for the second half of the data
Divide the data into quartiles
21, 23, 25, 25, 26, 26, 27, 28, 29, 29
Median of 2nd half: 26
7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29
14.5
Median
1st half
20.5
Median
Data set 26
Median
2nd half

10. The medians divide the data into four sections or quarters
7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29
14.5
Median
1st half
20.5
Median
Data set 26
Median
2nd half
Lower
Quartile
Middle
Quartile
Upper
Quartile
Quartiles
The medians divide the data into four sections or quarters

11. Least value
The smallest number in the data set 7
Greatest value
The biggest number in the data set 29
Number line
Use the least and greatest value to draw an adequate number line

12. Mark the least value: 7 with a point•

13. • • Mark the lower quartile: 14.5 with a vertical line
Connect the point and the line •

14. Mark the middle quartile: 20.5 with a vertical line•

15. • • Mark the upper quartile: 26 with a vertical line
Connect the tops and bottoms of the vertical lines •

16. Mark the greatest value: 29 with a point• •

17. Drawing information from a Box-and Whiskers Plot
3rd Quarter has a biggest range
Middle quartile: 50
Least value: 32
Upper quartile: 72
Greatest value: 80
Lower quartile: 45
2nd Quarter has the most concentrated data

18. Counting Outcomes and Theoretical Probability 4/22
The result of an action
An outcome or group of outcomes
Event
Sample Space
List of all possible outcomes

19. Theoretical
Probability
Number of favorable outcomes
Number of possible outcomes
Outcome you want
Total outcomes possible

20. Example
In the name:
Trisha Leanne McDowell
What is the probability of randomly choosing a vowel if the letters were scrambled?
Outcome you want (vowels)
Total outcomes possible (number of letters in name) 7 20
Try your name

21. Counting Principle
You cannot always count the possible outcomes
Multiplication can be used
Multiply the possible outcomes of each event

22. We use the last four digits of our Social Security Numbers for lots of things. How many unique combinations are possible?
Four digits so four events • • • 10 10 10 10
1st digit 2nd digit 3rd digit 4th digit
10000 possible unique combinations

23. WZZK is running a contest
WZZK is running a contest. If you call in and the last four digits of your Social Security Number are randomly generated, you will $1000.
What is the probability of winning?
Outcomes you want (your SS#)
Possible outcomes (all the combinations) 1
10000

24. You try
Workbook
Pages

25. Random Samples and Surveys 4/23
population
A group of objects or people
sample
Part of a population
Random Sample
Each member of a population has an equal chance of being selected in the sample

26. Example
Identify the population and 3 different sample groups
Elections are in November. Pollsters spend a lot of time and money to try and determine who is going to win.
Random sample: calling names out of the phone book
Not random sample: calling registered Republicans or Democrats

27. Fair Questions
A question that does not influence the sample
A question that makes one answer appear better than another
Biased Questions
Do you prefer sweet, loving doggies or mean, psychotic cats?
Example
Do you prefer cats or dogs

28. Workbook
Page

29. Independent and Dependent Events 4/26
Independent Events
The outcome of one event does not affect the outcome of another
Example
Rolling dice
Flipping Coins
Slot Machines
Lottery
Pulling marbles out of a bag and replacing them each time

30. Formula
The probability of A then B
P(A, then B) = P(A) •P(B)
Example
You roll a dice twice, what is the probability you roll a 4 then a 5?
P(4, then 5) = P(4) •P(5)
1 • 1
1/36

31. Dependant Events
The outcome of one event does affect the outcome of another
Example
Pulling marbles out of a bag and not replacing them
Counting Cards

32. Formula
The probability of A then B
P(A, then B) = P(A) •P(B after A)
Example
There are 4 red marbles and 6 blue marbles in a bag, what is the probability of pulling a red, then blue marble if none are replaced?
P(red, then blue) = P(red) •P(blue after red)
4 • 6
24/90
4/15

33. You Try
Workbook
Page

34. Permutations and Combinations 4/27
An arrangement where order is important
Notation
#choicesP#events
Example
Find the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters.

35. Because order matters, we're finding the number of permutations of size 2 that can be taken from a set of size 3. This is often written 3P2. We can list them as:
List
CA   CT   AC   AT   TC   TA
Math
3 • 2
Letter1 Letter2
6 possibilities

36. We have 10 letters and want to make groupings of 4 letters
We have 10 letters and want to make groupings of 4 letters. Find the number of four-letter permutations that we can make from 10 letters without repeated letters (10P4),
List
It is unrealistic to make a list
10 • 9 • 8 • 7
Math
Letter 1 Letter 2 Letter 3 Letter 4
5040 possibilities

37. You Try
4P2
6P4
9P4
10P8

38. Combination
An arrangement where order does not matter
Notation
#choicesC#events
Formula
Combinations are the number of permutations divided by (the number of events factorial)
#choicesC#events= #choicesP#events
#events!

39. Factorial
n!= n • (n-1) • (n-2) • (n-3) • . . .• 1
7! = 7 • 6 • 5 • 4 • 3 • 2 • 1
7! = 5040
6P4
Find 6C4 4!
6 • 5 • 4 • 3
4 • 3 • 2 •1 15

40. Example
Find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; AT is the same as TA.
Because order does not matter, we're finding the number of combinations of size 2 that can be taken from a set of size 3. This is often written 3C2. We can list them as:

41. List
CA   CT   AT
Math
# permutations 2! 6
2 • 1 6 2 3

42. You Try
4C2
6C4
9C4
10C8