Unit 4 - STATISTICS TOC How do you predict the winner of an election before the election takes place? In this lesson you will learn how to collect data about a
population by identifying a sample of the population. Lets Review Statistical questions are used to gather data about a population. How many texts do middle school students send in one
day? Core Lesson That could take a long time Core Lesson By surveying a sample of the group, you can make a generalization about the entire
group. Core Lesson The population is the entire group being studied. A sample is part of the population being surveyed. Core Lesson For example:
Predict the winner of the upcoming presidential election Population Sample American voters Adults walking to work Core Lesson
Another example: Tracking migration pattern of birds Population Sample A bird species Tagged birds In this lesson you have
learned how to collect data about a population by identifying a sample of the population. Guided Practice Identify the population and sample in the following survey: To gauge students preference for a new school mascot, the Student
Council President surveys her soccer team. Population Sample Extension Activities Answer the following questions. 1.You are buying ice cream for a party at your school, in which 700 students will attend. How would you use sampling to make a
generalization about students preferred ice cream flavors? 2.Why not survey all 700 students? 3.Describe the sample you would survey, and explain why you chose that sample. Quick Quiz Identify the population and the sample: 1. A telephone survey is given to 2,000
randomly selected families in order to predict the average amount of money American families spend on groceries each week. 2. To determine the number of students who carry backpacks in school, Tina collects data on the first 100 students who enter the building. Lets Review Statistical measures are then used to
analyze that data. How many texts do middle school students send in one day? Mean Median
Mode Range Interquartile Range Mean Absolute Deviation If you had to order t-shirts for your entire school, what sample would you choose to help you predict how many t-shirts of each size to order?
In this lesson you will learn how to identify representative samples by differentiating between biased and unbiased methods of sampling. Lets Review The population is the entire group being studied.
A sample is part of the population being surveyed. A Common Mistake Not all samples will lead to good predictions about an entire population. How tall are 7th graders?
Core Lesson ? Representative sample prediction based on data
accurate Valid inference Core Lesson Sampling method Unbiased Biased
Core Lesson This sample comes from a biased sampling method. It is not representative of the population. Core Lesson
This sample comes from an unbiased sampling method. It is representative of the population. Core Lesson Another example: Color of leaves in September a) 100 fallen leaves collected from the ground b) 100 leaves on tree branches c) 50 fallen leaves and 50 leaves on branches
d) 50 fallen oak leaves and 50 oak leaves on branches Core Lesson Unbiased sampling method Representative sample Valid inference
In this lesson you have learned how to identify representative samples by differentiating between biased and unbiased methods of sampling. Guided Practice A market researcher wants to know how 18-25 year old women spend their money. Which
group would be a representative sample? a) 18-25 year old women at the mall b) 18-25 men and women commuting to work c) Women of all ages commuting to work d) 18-25 year old women commuting to work Extension Activities In a complete paragraph, describe why the following sampling method is biased, and suggest an unbiased method.
You want to know your towns favorite fastfood restaurant. You randomly ask 30 people their preference as they leave one of the fast-food restaurants in town. Quick Quiz 1. An ice-cream company wants to find out if its ice cream is the favorite in the state. Which group would be a representative sample? a) Customers who visit their store b) Employees of ice cream stores in the state
c) People at the state fair d) Adults entering a gym in the capital city Quick Quiz 2. Which is an unbiased sampling method for predicting the type of payment most frequently used at a grocery store? Record the type of payment used by a) Students at the local high school b) Every 10th customer entering the store
c) Every 10th customer in the cash-only line d) Visa card holders Random Sampling The pick a name out of the hat technique Random number table Random number generator
TOC Systematic Sampling All data is sequentially numbered Every nth piece of data is chosen TOC Stratified Sampling
Data is divided into subgroups (strata) Strata are based specific characteristic Age Education level Etc.
TOC Convience Sampling Data is chosen based on convenience BE WARY OF BIAS! TOC Voluntary Response Sampling A sample which includes only willing participants
TOC Learning Task: Is It Valid? STANDARD ADDRESSED IN THIS TASK MCC7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that
population. Understand that random sampling tends to produce representative samples and support valid inferences TOC Complete each survey: (you have 8 min) There are 5 surveys around the room.
Quickly take each survey by placing your sticker on the appropriate answer. When finished, sit quietly and wait for instructions. TOC What color is your hair? Brown ______ Blond ______ Red ______ Black _______ Do you carry a cell phone? Yes______ No _________
About how many text messages do you send in a day? 0-20 _____ 21-40 ______ >40 ______ About how much time do you spend on homework? 0-15 min _____ 16-30 min _____ 31-45 min ______ 4660 min _______ > 60 min ______ What month were you born? Jan March _____ April June _____ July-Sept. _____Oct-Dec ______ TOC Using the survey results discuss the following vocabulary.
What is the population of your survey? The population is the entire class. Population is the entire set of items for which data can be collected. Did your class perform a census or a survey? A census means you ask everyone in the population. Survey means you ask a representative sample of the population. This is a census. How would you describe your results from question 2 as a
parameter for the population? A parameter means you describe a characteristic about the population based on your TOC data. The manager of the Millcreek Mall wants to know the mean age of the people who shop at the mall and the stores in which they typically shop. He hires Barker Market Research Company to collect the data. Dennis works for
the Barker Market Research Company and has been put in charge of collecting data for the Millcreek Mall. Dennis decides to interview 100 people one Saturday because it is the malls busiest shopping day. Is the survey a sample or a census? It is a sample. What is the population for this survey? The population is everyone who comes to the mall.
Is the sample size for the survey appropriate? The sample size is too small for the population. The 100 people are not a representative sample of the entire population. TOC In the summaries that follow, determine if the sample taken is representative of the
population without bias shown: TOC ABC Family is a television channel that targets families and young adults to view their station. ABC Family regularly posts online poll questions to their website. In 2010, ABC Family polled their viewers to ask about airing Rated R movies after 8pm on their channel. Almost 200,000 people
responded, and 85% of them disagreed with airing Rated R movies. Solution: Voluntary Response- ABC Family is only asking from data from their viewers, which may tend to be more conservative since it is a family targeted television station. TOC Mrs. Jones wants to know how the 5th grade feels about recess time. Mrs. Jones labels every
student in the 5th grade with a number. She then draws 50 numbers out of a hat and surveys these students. Mrs. Jones determines that 5th graders would like more recess time than they currently have. Solution: This is a Simple Random Sample (SRS). Mrs. Jones gave each child in the 5th grade the same chance of being selected. TOC
The City of Smallville wants to know how its citizens feel about a new industrial park in town. Surveyors stand in the Smallville Mall from 8am-11am on a Tuesday morning and ask people their opinion. 80% of the surveyed people said they disagreed with a new industrial park. Solution: This is convenience sampling. People at a mall are easy to reach, but not every individual in Smallville has an equal chance of
being chosen. For example, people that work and are not at the mall on Tuesday morning have no TOC chance of being chosen. The National Rifle Association (NRA) took a poll on their website, www.nra.com, and asked the question, Do you agree with the 2nd Amendment: the Right to Bear Arms? 98% of the people surveyed said Yes, and
2% said No. Solution: This is voluntary response. The NRA only asked people on their website, which are more likely to be pro 2nd amendment. TOC Biased or The mayor surveys 100 supporters at a rally about the most important issues
to be addressed by the city council. Unbiased? The principal sends out questionnaires to all of the students to find out what kind of music students prefer at dances. The owner of a record shop surveys only customers over the age of 18 who shop at his store. The teacher writes the name of each student on a piece of paper and questions the students whose names are drawn. A convenience store surveys customers one morning to determine what products they may like the store to stock.
Each students name is written on a slip of paper and placed in a box. One slip of paper is selected to determine the student to be the homeroom TOC representative. Biased or Unbiased? A company randomly selects 500 customers from its database and then surveys these customers to find out how they like their service. Unbiased A city-hall employ surveys 100 customers at a restaurant
to learn about the jobs and salaries of city residents. Biased A newspaper randomly chooses 100 names from a subscriber database and then surveys those subscribers to see if they read the restaurant reviews. Unbiased TOC Predicting Proportion: sample
piece sample size x (prediction) entire population
TOC x = 2550 students Example: A university has 30,600 students. In a random sample of 240 students, 20 speak 3 or more languages. Predict the number of students at the university that speak 3 or more languages. TOC
There are 4500 elk located on a preserve in Colorado. A biologist thinks that the herd may be infected with parasite. She does a random sample of 50 elk. If she discovers that 8 of the sample is infected. Predict how many elk the biologist can expect to be infected. 720 elk are infected
TOC A factory produces 150,000 light bulbs per day. The manager estimates that less than 1,000 defective bulbs are produced each day. In a random sample of 250 light bulbs, there are 2 defective bulbs. Determine if the manager's estimate is likely to be accurate. Explain. His estimate is incorrect. There
are at least 1200 defective bulbs each day. TOC A middle school has 2,500 students. Morgan interviewed 75 students about their library habits. She found that 45 of the students checked out a book weekly. Predict the number of students likely to check out books weekly.
1500 students TOC Yes. 56 students have traveled. Zack chooses a random sample of 50 out of 400 students. He finds that 7 of them have traveled to a foreign country. Zack claims that more than 50 of the 400 students have traveled to a foreign country. Do you agree
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