Day Topic(s) 1

Stat Intro: Gather Data and Graphing Calculator Functions

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Stat Lab Day 1: Form Groups, choose topics, begin work

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Stat Lab Day 2: Working Session

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Probability Answers

Casino Lab Part 1 5

Casino Lab Part 2

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The Normal Curve

Date _________ Period_________

Unit 12: Statistics and Probability

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The following questions were posed by students. The answers to these questions will generate the data that we will analyze. Please answer every question and then pose 3 more of your own… 1. How old will you be when you graduate from high school?

2. How many times have you traveled outside the continental United States?

3. How many computers do you have?

4. What is your resting heart rate?

5. What is the age difference between your parents?

6. How many siblings do you have?

7. How many pets do you have?

8. How many sports do you play?

9. How many notebooks/binders are in you backpack?

10. How many pencils are in your pockets?

11. How many hours do you go on Facebook per week?

12. How many hours do you sleep each night?

13. On average, how many texts do you send/receive per day?

14. How many children would you like to have in the future?

15. How many songs on your ipod do you have that start with the letter b?

16. Amount of cash to nearest dollar on you right now.

17. How many pairs of jeans do you currently own?

18. How many hours of TV do you watch each week?

19. How many books have you read since the school year started?

20. How many songs do you have on iTunes?

21. How many items do you currently have on your key chain?

22. How many items do you usually purchase at or bring for lunch?

23. How many times have you been bitten by an animal?

24. How many accessories are you currently wearing?

25. How many days of school have you missed so far this year?

26. How many U.S. states have you visited?

27. How many haircuts have you had since the start of school?

28.

29.

30.

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Leave blank for now….

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Let’s choose one of the above topics to analyze in class today. List the data below…

STAT LIST Sort: Mode:

1 – Var STATS

Mean: Standard Deviation: 5 Number Summary:

BOX PLOT Modified Box Plot: IQR & Outliers:

HISTOGRAM SKEWED (more on this in the SOCS handout, page 8)

Left: Symmetric: Right:

Unit 12 Day 1: Gathering Data & Calculator Fun!

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The following Stat Project is due before the start of class on Tuesday, June 8. The project consists of 3 sections. Introductory Questions Analyzing 2 data sets Additional Box Plot Analysis

General Lab Directions The final project should be typed (Word or Powerpoint) and submitted electronically. You only need

to submit one file per group. All graphs must be well labeled and neat. You may draw the graph by hand and scan it if you want,

or you can use excel or some other graphing program Neatness, organization, spelling, creativity will be factored into your grade. Content matters. Answers must make sense and be written at an honors level

The following worksheets can be used to gather and organize your thoughts – you will have to transfer all of the information into your final electronic file, but this will guide your efforts. For each topic, you must analyze in accordance with SOCS (reference guide follows – page 8)

Unit 12 Day 2: Stat Project Part 1

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Statistics is about variation. Data vary because we don’t see everything and because even what we do see and measure, we measure imperfectly. So in a very basic way, Statistics is about the real, imperfect world in which we live. [Stats: Modeling the World, Bock et al, p. 6] Note: Data – Plural Form; Datum – Singular Form Answer the following questions before you begin analyzing your data. There are no right or wrong answers. Use your common sense and explain your reasoning. You can write your answers here, but be sure to type them in your final electronic file.

1. List 3 specific reasons a company/organization might write a survey and gather real data? What answers are they trying to ascertain?

2. Recently Gatorade recruited young athletes around the country to create focus groups for new flavor research. Focus groups are simply groups of people who are asked their opinion for such things as trying a new product, watching a new movie or discussing a current event such as the recent oil spill.

Why would a company/organization pay people for their opinions?

3. Why do companies/organizations spend great quantities of money to make sure that the data they gather on a certain product/movie/current event are accurate? (Most statisticians make big bucks.)

Stat Lab Part 1: Introductory Questions

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In this section you are going to analyze two sets of data that we collected in class. You can choose which two of the ten that you are most interested in analyzing. Again, your final submission must be typed. Use the following sections to organize your thoughts… Data Topic #1: __________________________________________ (list data below) Data Topic #2: __________________________________________ (list data below) For each data set you must include the following… (use this as a check list!) * Note: the rubric I will use is posted on the class website if you want to see how you will be graded Mean, Median, Mode 5 Number Summary IQR and Outliers Standard Deviation Histogram (Modified) Box Plot Analysis of each set individually (see guided questions below) Comparison of the two data sets.

1. Overall analysis (one for each set) Describe The Data (Reference handout on SOCS – interpret the results don’t simply list them. Describe things in context.) Answer the following regarding your first set of data.

2. Did anything surprise you about this data?

3. Do you see a trend within the data? Make a prediction relevant to the data. Thoroughly describe why

your prediction makes sense or flaws in your prediction. (Even if you are using class data – try to be creative and thoughtful here – no lazy thinkers).

4. How do your two data sets compare and contrast?! (Possible ideas: compare the graphs, look at the important values that you calculated, write a few sentences comparing the topics themselves… This is open-ended and may vary in difficulty based on the two topics you chose. Be creative!)

Stat Lab Part 2: Data Analysis

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In this section you will create two Box plots on the SAME AXIS. Again, use this space to guide your work, but type or scan it into your final document! You will use two sets of data – one is provided for you and one you must Google! Data Set #1: High Temperatures from May 1 – May 30, Ocean City, NJ (weather.com) 91 87 84 83 78 85 71 84 59 62 59 61 63 85 75 72 68 49 66 74 84 73 69 68 75 68 80 64 70 79 Data Set #2: Choose any city NOT in the USA and list its high temperatures for the month of May. (Find a city that has very different temperatures from Ocean City – outliers would be great). 5-Number Summary for Ocean City___________________________________ 5-Number Summary for City of your Choice____________________________ Create Side by Side Boxplots below (modified for outliers). Create one number line and include LABELS. Rule for Outliers - 1 1.5*Q IQR or 3 1.5*Q IQR

1. How can you determine visually which city has greater variability in its high temperatures?

2. Which city has the highest high temperature?

3. Determine what an outlier would be for Ocean City in the month of May. Show all work!

4. If you heard a commercial claiming, “Come to Ocean City in May, our average temperature is 71

degrees!” Do you feel confident that you would get a 71 degree day? What if they stated the median temperature? Explain thoroughly.

Stat Lab Part 3: Additional Box Plot Analysis

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Shape – What it looks like? Common descriptors: symmetrical, uniform, skewed left, skewed right. Outliers – Data points that are positioned away from the body of the distribution. Stragglers. Boxplots: there is a formula or simply graph a modified boxplot (*). Histograms: more experiential and don’t have a rule.

Center – If a distribution is symmetrical and unimodal this is easy. Use mean or median they will be

very close. Otherwise, it’s tricky. Follow the following: Boxplots: report median Histograms: report mean if symmetrical; otherwise, report mean and median. Spread – This is all about variation! Consider the temperatures of Philly and Honolulu over 6 days. Philly 91 62 84 78 89 82 x = 82 Honolulu 82 83 83 81 82 81 x = 82 Both cities have the same average but Philadelphia has a much greater variation or spread. Our

weather varies greatly sometimes day to day. Consider: Are the data tightly clustered around the center or spread out? Boxplots: Report IQR Histograms: Report standard deviation

LEFT-SKEWED Histogram: The outliers to the left are pulling the shape to the left. Important: In a left-skewed distribution Mean < Median.

RIGHT-SKEWED Histogram: The outliers to the right are pulling the shape right. Important: In a left-skewed distribution Mean >Median.

ShapeOutliersCenterSpread is an acronym helps to guide us when describing a distribution

The low scores “wreck” the mean

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Probability as defined as the likelihood an event will occur. Ex: P (A on Stat Test) = Probabilities range from 0 (impossible) to 1 (definite). When all outcomes are equally likely, the theoretical probability that an event A will occur is

Number of outcomes in event A

( )Total number of outcomes

P A

Example 1: You rolled a six-sided die. Find the probability of (a) rolling a 5 and (b) rolling an even number. Example 2: You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event. a. A perfect square is chosen b. A factor of 30 is chosen. If A and B are any two events, then the probability of A or B is ( ) ( ) ( ) ( )P A or B P A P B P A and B If A and B are disjoint events (have no chance of overlap) then the probability of A or B is: P(A or B)= P(A) +P(B) Example 3: A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10 or a face card? Example 4: A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a face card or a spade? (be careful, there is overlap here).

Unit 12 Day 3: Probability Overview, Compound Events & Conditional Prob.

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If A and B are independent events, then the probability that both A and B occur is: P(A and B) = P(A) P(B) Example 5. For a fundraiser, a class sells 150 raffle tickets for a mall gift certificate and 200 raffle tickets for a booklet of movie passes. You buy 5 raffle tickets for each prize. What is the probability that you will win both prizes? If A and B are dependent events, then the probability that both A and B occur is P(A and B)= P(A) P(B|A) (this just means the P(A) P(B) given that A has already occurred. In other words, without replacement! Example 6: You randomly select two cards from a standard deck of 52 cards. What is the probability that the first card is not a heart and the second is a heart if (a) you replace the first card before selecting the second card, and (b) you do NOT replace the first card? Answers:

1. 1 1,

6 2 2. 1 3

,5 10

3. 4

13 4. 11

26 5. 1

1200 6. 3 13

,16 68

Reference Guide for the difference between Disjoint Events and Independent Events on next page

Helpful Hint:

AND = x (multiply)

OR= + (add)

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One Event

( ) ( ) ( )P A or B P A P B

("3" ) ("3") ( ) ("3" )

1 3 1 3 1

6 6 6 6 2

P or Odd P P Odd P and Odd

( ) ( ) ( ) ( )P A or B P A P B P A and B

Subtract the overlap! When there is Overlap…

When there is NO Overlap…

Example: Rolling one die and rolling a “3” or and Odd #.

Example: Rolling one die and rolling a “3” or and Even #.

("3" ) ("3") ( )

1 3 4 2

6 6 6 3

P or Even P P Even

Two Events

Independent: There’s no “memory”

Example: Rolling two dice… First a “5” and then a “2”.

( ) ( ) ( )P A then B P A P B

("5" "2") (5) (2)

1 1 1

6 6 36

P then P P

Dependent: The first event affects the second event Example: Drawing 2 cards…

An Ace then a King

( ) ( ) ( assuming Ace was Taken)

4 4 40.006

52 66351

P Acethen King P Ace P King

( ) ( ) ( )P A then B P A P B A

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Rules of Craps! Win Lose Other Come out roll(s) 7 or 11 2, 3, or 12 4, 5, 6, 8, 9, 10 Establishes the Point!

“Point” Roll(s) Hit the Point 7 All other #s Reroll!

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For the Casino Lab, you must complete the craps station, and Blackjack or Roulette. The lab is due Monday!

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Let’s recap what a standard deviation is… A z-score is defined as the _________________ of standard deviations a score is from the _____________. The formula for a z-score is: Ex 1: A set of values has a mean of 85 and a standard deviation of 6. Find the z-score of the value 76. z-scores are closely related to the ___________________ curve, or normal distributions. Typically, data sets > 1000 tend to be normalized. For example, SAT or IQ scores. Example: IQ test

100

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x

Score: from mean:

z-score: Empirical Rule:

Unit 12 Day 6: Z-Scores & The Normal Distribution

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Example 1: In a survey, the responses to the question “How much time do you spend at meals in one week?” are normally distributed. The mean was 13 hours, the standard deviation was 3 hours.

a. What values are one standard deviation from the mean?

b. What percent of the responses would you expect to find from 10 hours to 16 hours?

c. Suppose there are 100 responses to the survey question. How many responses would you expect to be values from 10 hour to 16 hours?

d. Of the 100 responses, how many would you expect to be values from 16 hours to 19 hours? Example 2: In a university lecture class where the final exam scores have a mean of 68 and a standard deviation of 7. The grades on the exams are all whole numbers and the grade pattern follows a normal curve.

a. What percent of students above 68?

b. Find the number of students who receive grades from 61 or below. Example 3: The mean of a data set is 7 hours and the standard deviation is two. About what percentage of students have an amount of homework within 2 standard deviations of the mean?