TOC

Unit 4 - STATISTICS

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

populationby identifying a sample of

the population.

Let’s Review

How many texts do middle school

students send in one day?

Statistical questions are used togather data about a population.

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 groupbeing studied.

A sample is part of the population being surveyed.

Core Lesson

For example:Predict the winner of the upcoming

presidential election

Adults walking to work

American votersPopulation

Sample

Core Lesson

Another example:Tracking migration pattern of birds

Tagged birds

A bird speciesPopulation

Sample

In this lesson you have learned how to collect data

about a populationby 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.

Let’s Review

How many texts do middle school students send in

one day?

Mean Median Mode

Range

Interquartile Range

Mean Absolute Deviation

Statistical measures are then used to analyze that data.

If you had to order t-shirts for your entire school, what sample would you choose to

help you predict how manyt-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.

Let’s Review

The population is the entire groupbeing studied.

A sample is part of the population being surveyed.

A Common MistakeHow tall

are 7th graders?Not all samples will lead to good predictions about an entire population.

Core Lesson

Representative sample

Valid inference

?accurate

prediction based on

data

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 groundb) 100 leaves on tree branchesc) 50 fallen leaves and 50 leaves on branchesd) 50 fallen oak leaves and 50 oak leaves on branches

Core Lesson

Representative sample

Valid inference

Unbiased sampling method

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 mallb) 18-25 men and women commuting to workc) Women of all ages commuting to workd) 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 town’s favorite fast-food 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 storeb) Employees of ice cream stores in the statec) People at the state faird) 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 schoolb) Every 10th customer entering the storec) Every 10th customer in the cash-only lined) Visa card holders

TOC

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.

Use random sampling within each strata

TOC

Convience Sampling

Data is chosen based on convenience–BE WARY OF BIAS!

TOC

A sample which includes only willing participants

Voluntary Response Sampling

TOC

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

Learning Task: Is It Valid?

TOC

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.

Complete each survey: (you have 8 min)

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 ______ 46-60 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 ofitems 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

parameterfor the population? A parameter means you describe a

characteristic about the population based on your data.

Most seventh grade students carry a cell phone.

TOC

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 mall’s 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

chance of being chosen.

TOC

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

The mayor surveys 100 supporters at a rally about the most important issues to be addressed by the city council.

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 student’s 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

representative.

Biased or Unbiased?

TOC

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

Biased or Unbiased?

TOC

Predicting Proportion:sample piece sample size

x (prediction)

entire population

TOC

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.

x = 2550 students

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

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

with his answer? Explain.

Yes. 56 students have traveled.