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

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

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?

A Statistics Review Game Greed A Statistics Review Game

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

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

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

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

Calculate your score Round Score 1 2 3 4 5 total

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

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

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

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

Calculate your score Round Score 1 2 3 4 5 total

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)

NONE. Homework

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

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

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

Choice 3

Discuss this as a class

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

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

WORKSHEET Graphs Homework

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?

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

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

Just Watch!!!!!!!!! Find the standard deviation by hand i xi Xi- 1 12 15 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

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

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

Pg. 702 2, 4, 6, 7 Homework

The Normal Distribution 16-4

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

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. - 3 -2 -1 mean 1 2 3 68% 13.5% 2.35% 95% 99.7%

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.

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

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 3000 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?

Pg 708 15-18 Homework

16-5 Sampling

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.

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

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?

Pg 713 evens Homework

Simulations 16-7

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?

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

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

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?

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?

Worksheet Homework

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

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

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.

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

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

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

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

Determining best method The table below represents the yield per plot. You will need this to determine which method is best and why. 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

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

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?

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

Distracted Driver Project

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?

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?

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?

None Homework