1. DATA and Probability 7/20/2018 3:44 PM
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

2. 7/20/2018 3:44 PM
Statistics
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

3. Calculate your height in inches
Calculate your height in inches. Place it on a sticky note and place it on the board in numeric order:
Heights:

4. Terms Mean: Average Median: Middle of an ordered list
Exact middle for an odd # of items
Average of the middle two for an even # of items
Mode: Most frequent
Range: Highest – Lowest
Q1: median of the lower half of the data
Q3: median of the upper half of the data

5. Stem & Leaf or Stem Plot
Displays all data
Stem Leaf
1st #(s) Last #

6. Use the height data to: Create a stem plot with the data
Use the stem plot to find the
Mean
Median
Mode
Range Q1 Q3

7. Box & Whisker
Helps you to see where the data lies, as each part is 25% of the data
Lowest and highest values = endpoints
Median of the data = center of the box
Median of the lower part and upper part = edges of the box

8. Box & Whisker Plot IQR = Q3 – Q2
low Q median Q high
lowest 25% nd 25% rd 25% highest 25%
the box contains 50% of the data
IQR = Q3 – Q2
Outliers are IQR from the ends of the box
Extreme Outliers are 3∙IQR from the ends of the box
The high and the low are not always Outliers, not all data sets contain outliers.

9. Use the height data to:
To create the box and whisker plot for the heights

10. Make the calculations for and draw a boxplot of the following data
Draw boxplot for the following test scores:
98, 75, 80, 74, 92, 88, 30, 83, 60, 72, USE THE CALCULATOR
Determine if there are any outliers in the data.
Ordered list: 30, 60, 72, 74, 75, 80, 83, 88,92, 98, 99
Draw a number line
Plot the end points
Find the median
Find the median of the first half
Find the median of the second half
Draw the box around the “three” medians
Connect the box with “whiskers” to the endpoints

11. Box & Whisker Skew is determined by the tail
Relatively evenly distributed (normal) data
Skewed left (longer left tail)
Skewed right (longer right tail)
Skew is determined by the tail

12. Dot Plot
Similar to a stem and leaf plot but does not necessarily retain the precise values of the data
Given: 10, 18, 21, 26, 30, 31, 38, 40
Create both a stem and leaf and a dotplot then check your answer below
Stem and Leaf Dot Plot
1 0, 8
2 1, 6
3 0, 1, 8
4 0

13. Using Graphs to make Predictions
You will need to interpret /predict from:
Circle Graphs
Line Graphs
Bar Graphs
Box-and-Whiskers
Stem and Leafs / Stemplots
Scatter Plots
Equations/Graph of Best Fit

14. How many people were surveyed?
How many more people like R & B than hip hop?

17. A bag is filled with marbles
A bag is filled with marbles. Among the marbles, 1/3 are red, a fourth are blue, 5% are white, a fifth are black and a sixth are yellow:
Which sections represents each color?
Red
Blue
White
Black
Yellow

18. Probability

19. How can we determine all the possible outcomes of a given situation?
TREE DIAGRAM—an illustrative method of counting all possible outcomes.
List all the choices for the 1st event
Then branch off and list all the choices for the second event for each 1st event, etc.

20. A restaurant offers a salad for $3. 75
A restaurant offers a salad for $ You have a choice of lettuce or spinach. You may choose one topping, mushrooms, beans or cheese. You may select either ranch or Italian dressing. How many days could you eat at the restaurant before you repeat the salad?
ranch
Italian
mushrooms
beans
cheese
Lettuce
spinach

21. While the tree diagram is beneficial in that it lists every possible outcome, the more options you have the more difficult it is to draw the diagram. Fundamental counting Principle—is a mathematical version of the tree diagram, it gives the # of possible ways something can be accomplished but NOT a list of each way.

22. _______ ______ _______ pants shirts shoes
Example:
Jani can choose from gray or blue jeans, a navy, white, green or stripped shirt and running shoes, boots or loafers? How many outfits can she wear?
_______ ______ _______
pants shirts shoes 2 4 3
=24

23. Permutations—all the possible ways a group of objects can be arranged or ordered (the way things are listed matters) Example: There are four different books to be placed in order on a shelf. A history book (H), a math book (M), a science book (S), and an English book (E). How many ways can they be arranged? 24 WAYS 4 • 3 • 2 • 1 = 24
H, M, S, E
M, E, S, H
S, M, E, H
E, M, S, H
H, M, E, S
M, E, H, S
S, M, H, E
E, M, H, S
H, S, E, M
M, S, H, E
S, H, M, E
E, H, M, S
H, S, M, E
M, S, E, H
S, H, E, M
E, H, S, M
H, E, M, S
M, H, E, S
S, E, M, H
E, S, M, H
H, E, S, M
M, H, S, E
S, E, H, M
E, S, H, M

24. A permutation of n objects r at a time follows the formula
This can be done on your calculator with the following keystrokes:
Type the number before the P
Press math
Over to prb
Choose number 2 nPr
Enter the number after the P
Press enter.
Now Try 8P3

25. How can you determine the difference between a permutation and a combination?
Combinations—the number of groups that can be selected from a set of objects --the order in which the items in the group are selected does not matter

26. Example: How many three person committees can be formed from a group of 4 people—Joe, Jim, Jane, and Jill
Joe, Jim , Jill
Joe, Jill, Jane
Joe, Jim Jane
Is Joe, Jane, Jim
A different committee
Jim, Jane, Jill
Formula:
For the problem above:
Using the same basic steps on the calculator but choosing nCr find
8C3
Is there a difference in value for 8C3 and 8P3

27. Combinations
This can be done on your calculator with the following keystrokes:
Type the number before the C
Press math
Over to prb
Choose number 3 nCr
Enter the number after the C
Press enter.
Using the same basic steps on the calculator but choosing nCr
find 8C3
Is there a difference in value for 8C3 and 8P3

28. Replacement—being allowed to use the same object again (nr) Example: try each before checking The keypad on a safe has the digits 1- 6 on it how many: a) four digit codes can be formed _____ _____ _____ _____ b) four digit codes can be formed if no 2 digits can be the same 6 6 6 6 6 5 4 3

29. —occurs when you have identical items in a group Example:
Repetition
—occurs when you have identical items in a group
Example:
Find all arrangements for the letters in the word
TOOL ____ ____ ____ ____
TOOL OLOT LOTO
TOLO OLTO LOOT
TLOO OTOL LTOO
OTLO
OOTL
OOLT
We would expect 24
but since you can’t distinguish between the two O’s all possibilities with the O’s switched are removed we divide by the number of individual repetitions—that is 24/2 = 12 which is what we have 4 3 2 1

30. Formula for repetitions:
where s and t represent the number of times different items are repeated
EXAMPLE: try then check
How many ways can you arrange the letters in BANANAS
A’s N’s
The factorial key is found by pressing math and arrowing over to PRB

31. If all outcomes are successful, the probability will be 1 If no outcomes are successful, the probability will be 0 So Probability is 0 ≤ P ≤ 1

32. What is the probability of getting an ace from a deck of 52 cards
What is the probability of getting an ace from a deck of 52 cards? 4 aces so What is the probability of rolling a 3 on a 6 sided die? there is one 3 on 6 sides so

33. Try each then check: What is the probability of rolling an even number
Try each then check: What is the probability of rolling an even number? 2,4, 6 are even so What is the probability of getting 2 spades when 2 cards are dealt at the same time? at the same time indicates the use of a combination —hint there are 13 spades

34. What is the probability of getting a total of 5 when a pair of dice is rolled?
Draw the following chart for the sum of all rolls and count how many have a sum of 5 + 1 2 3 4 5 6 7 8 9 10 11 12

35. Compound Probability
What is meant by compound probability?
The words or & and are in the problem
OR: P(A or B) = P(A) + P(B) – P(A and B) Example: What is the probability of getting a 2 or a 5 on the roll of a die? Exclusive Events: events that do not have bearing on each other

36. What is the probability of drawing an ace or a heart
What is the probability of drawing an ace or a heart? ace + heart – ace of hearts + - = Events are inclusive if they have overlap!

37. AND: indicates multiplication Examples: What is the probability of tossing a three of the roll of a die and getting a head when you toss a coin? three and a head * = These events are independent—have no effect on the outcome of the other