1. Unit 4 - STATISTICS
Data is chosen based on being readily available. Runs the risk of being severely biased because no real statistical method is used in order to choose the data. For example if you want to find out if people shop in a certain shopping mall your sample is going to be extremely biased if you stand outside of that mall and survey people as they walk in.
Sarah DiCalogero - Statistical Sampling

2. How do you predict the winner of an election before the election takes place?
Often we’d like to know information before it is available, or when it would be difficult or time-consuming to collect the information.

3. In this lesson you will learn how to collect data about a population
by identifying a sample of the population.

4. Statistical questions are used to gather data about a population.
How many texts do middle school students send in one day?

6. By surveying a sample of the group, you can make a generalization about the entire group.

7. The population is the entire group being studied.
A sample is part of the population being surveyed.

8. Predict the winner of the upcoming presidential election
For example:
Predict the winner of the upcoming presidential election
The population is the group we would like to know information about, in this case, American voters. We want to know who they plan to vote for.
The sample is the part of the population we plan to gather data from, in this case, adults walking to work.

9. Tracking migration pattern of birds
Another example:
Tracking migration pattern of birds
The population is the group we would like to know information about, in this case, American voters. We want to know who they plan to vote for.
The sample is the part of the population we plan to gather data from, in this case, adults walking to work.

10. In this lesson you have learned how to collect data about a population
by identifying a sample of the population.

11. 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.
The population is the group we would like to know information about, in this case, the students in the school. We want to know what type of mascot they would prefer.
The sample is the part of the population we plan to survey, in this case, the students on the President’s soccer team.

12. Answer the following questions.
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?
Why not survey all 700 students?
Describe the sample you would survey, and explain why you chose that sample.

13. 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.

14. Statistical measures are then used to analyze that data.
Mean Median Mode
Range
Interquartile Range
Mean Absolute Deviation

15. t-shirts of each size to order?
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?
LearnZillion Notes:
--This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific. For example, the hook could be “How do you know if 2/3 is greater than 5/8?” rather than something more generic such as “How do you compare fractions?”
--You can fill in an example using the blue text or you can delete that text box and include some other image that explains what you’re talking about.

16. LearnZillion Notes:
--This is our lesson objective. Keep it as short and student-friendly as possible. Put what they will learn in green and then how they’ll learn it in blue. For example, “In this lesson you will learn how to compare fractions with different denominators by using a number line.”

17. The population is the entire group being studied.
A sample is part of the population being surveyed.

18. How tall
are 7th graders?
It looks like this sample was chosen because they were the first people in line. Do you think this sample represents the entire population?

19. prediction based on data LearnZillion Notes:
--The Core Lesson may take more than one slide. You can add as many of these slides as you like. Simply click on “New Slide” and then select the Core Lesson template slide to add a new one.
--Feel free to move or resize the blue text box to fit your content.

20. Unbiased sampling method: Sample doesn’t favor a particular outcome
Biased sampling method: Sample favors a particular outcome

21. Your principal is ordering t-shirts for the all the students at your school. In order to determine what size t-shirts to order, the principal plans on surveying a sample of students about what size t-shirt they wear. The principal surveys 30 members of the football team about their t-shirt sizes. Is this a representative sample?

22. Your principal is ordering t-shirts for the all the students at your school. In order to determine what size t-shirts to order, the principal plans on surveying a sample of students about what size t-shirt they wear. The principal surveys 30 members of the football team about their t-shirt sizes. Is this a representative sample?

23. Another example: Color of leaves in September
100 fallen leaves collected from the ground
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

24. Your principal is ordering t-shirts for the all the students at your school. In order to determine what size t-shirts to order, the principal plans on surveying a sample of students about what size t-shirt they wear. The principal surveys 30 members of the football team about their t-shirt sizes. Is this a representative sample?

25. LearnZillion Notes:
--This is the lesson conclusion. On this slide you’ll change your original lesson objective to past tense and explain what the student has just learned. You can retype it here or you can delete the text on this slide and then just copy and paste the text box from the original Lesson Objective slide and then edit it to make it past tense!

26. a) 18-25 year old women at the mall
A market researcher wants to know how year old women spend their money. Which group would be a representative sample?
a) year old women at the mall
b) men and women commuting to work
c) Women of all ages commuting to work
d) year old women commuting to work
LearnZillion Notes:
--The “Guided Practice” should include 1 practice problem that targets the skill that was used in the Core Lesson. Use the same vocabulary and process you used in the original lesson to solve this problem. You’ll be making a video in which you solve this question using your tablet and pen, so all you need to do is write the question on this slide.

27. 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.
LearnZillion Notes:
--On the Extension Activities slide(s) you should describe 2-3 activities written with students as the audience (not teachers). Each extension activity should push the students a bit further with the lesson but in a different application or context. Each activity should be designed to take roughly minutes. Teachers will likely display the slide in class and then assign an activity to a student or group for additional practice and differentiation. Ideally, these Extension Activities will be created such that a teacher can differentiate instruction by giving more difficult extension activities to students who have shown mastery of the lesson, and less difficult activities to students who are not yet proficient.
--If you need more than one slide to list your extension activities, feel free to copy and paste this slide!

28. Customers who visit their store
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?
Customers who visit their store
Employees of ice cream stores in the state
People at the state fair
Adults entering a gym in the capital city
LearnZillion Notes:
--”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.

29. Record the type of payment used by… Students at the local high school
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…
Students at the local high school
Every 10th customer entering the store
c) Every 10th customer in the cash-only line
d) Visa card holders
LearnZillion Notes:
--”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.

30. The “pick a name out of the hat” technique
Random Sampling
The “pick a name out of the hat” technique
Random number table
Random number generator
A simple random sample of n pieces of data from a population of data is collected in such a manner such that every sample has an equal chance of being selected and included in the sample. The data is chosen randomly using either a random number table or a piece of software called a random number generator.
Sarah DiCalogero - Statistical Sampling

31. All data is sequentially numbered Every nth piece of data is chosen
Systematic Sampling
All data is sequentially numbered
Every nth piece of data is chosen
A simple random sample of n pieces of data from a population of data is collected in such a manner such that every sample has an equal chance of being selected and included in the sample. The data is chosen randomly using either a random number table or a piece of software called a random number generator.
Sarah DiCalogero - Statistical Sampling

32. Data is divided into subgroups (strata)
Stratified Sampling
Data is divided into subgroups (strata)
Strata are based specific characteristic
Age
Education level
Etc.
Use random sampling within each strata
All of the data is divided into distinct subgroups or strata, based on a specific characteristic such as age, income, education level, and so on. All members of a stratum share the specific characteristics. Random samples are drawn from each stratum.
Sarah DiCalogero - Statistical Sampling

33. Data is chosen based on convenience BE WARY OF BIAS!
Convience Sampling
Data is chosen based on convenience
BE WARY OF BIAS!
Data is chosen based on being readily available. Runs the risk of being severely biased because no real statistical method is used in order to choose the data. For example if you want to find out if people shop in a certain shopping mall your sample is going to be extremely biased if you stand outside of that mall and survey people as they walk in.
Sarah DiCalogero - Statistical Sampling

34. Voluntary Response Sampling

35. 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

36. 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.

37. 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 _____ ______ >40 ______
About how much time do you spend on homework? 0-15 min _____ min _____ min ______ min _______ > 60 min ______
What month were you born? Jan – March _____ April – June _____ July-Sept. _____Oct-Dec ______

38. 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 data.
Most seventh grade students carry a cell phone.

39. 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.

40. In the summaries that follow, determine if the sample taken is representative of the population without bias shown:

41. 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.

42. 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.

43. 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.

44. The National Rifle Association (NRA) took a poll on their website, www
The National Rifle Association (NRA) took a poll on their website, 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.”

45. Biased or Unbiased?
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.

46. 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

47. Predicting Proportion:
x (prediction)
sample piece
sample size
entire population

48. 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.

49. There are 4500 elk located on a preserve in Colorado
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

50. A factory produces 150,000 light bulbs per day
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.

51. A middle school has 2,500 students
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

52. Zack chooses a random sample of 50 out of 400
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 with his answer? Explain.