7.SP.A.2-Sampling in Action: Making Predictions with Data

6.SP1 LESSON: Categorical and Numerical Data

Poll

A. Heights of 20 Sixth Graders

• CATEGORICAL

• NUMERICAL

Poll

B. Favorite flavor of ice cream for 10 sixth graders

• CATEGORICAL

• NUMERICAL

Poll

C. Hours of sleep recorded by 30 sixth graders

• CATEGORICAL

• NUMERICAL

Poll

D. Eye color for 30 sixth graders

• CATEGORICAL

• NUMERICAL

DISPLAYING DATA: DOT PLOTS

To answer statistical questions we collect data. Numerical data can be summarized using dot plots.

Multiple Choice

What is the shape of the dot plot shown?

• skewed left

• skewed right

• symmetrical

Multiple Choice

The bar graph shows the approximate number of visitors at a state park. What fraction of the total visitors visited in 2008 and 2009 combined? Express in simplest form.

• 3/20

• 13/40

• 7/40

• 65/100

Multiple Choice

The bar graph shows the approximate number of visitors at a state park. What percentage of visitors went to a state park in 2011? Hint: Percent proportion

• 20%

• 40%

• 60%

• 80%

Multiple Choice

Remember: part over whole

• 4/10

• 2/5

• 6/10

• 3/5

Multiple Choice

What type of graph is this?

• Bar Graph
• Histogram
• Line Plot

Multiple Choice

Which interval has 400 employees?

• 33-43
• 0-10
• 77-87
• 66-76

Multiple Choice

How many cities have temperatures between 70 degrees and 99 degrees?

• 44
• 34
• 26
• 62

Multiple Choice

How many students are between 48 and 51 inches tall?

• 14
• 8
• 2
• 0

Multiple Choice

How many people watched between 6 and 10 hours of TV last week?

• 31
• 22
• 15
• 35

Multiple Choice

More people had between __ and __ cups of coffee than any other range.

• 0-3
• 8-11
• 12-15
• 16-19

Multiple Choice

How many students were greater than or equal to 60 inches tall?

• 21
• 11
• 17
• 6

Multiple Choice

Mr. Semo is making a histogram to show the scores on the last science test. He first lists the scores in a stem-and-leaf plot. How many units tall should the bar be for the interval 70-79?

• 2
• 5
• 9
• 11

Multiple Choice

How many students have a shoe size bigger than 8?

• 2

• 3

• 4

• 9

Multiple Choice

What was the day with the most amount of cars sold?

• Friday

• Tuesday

• Wednesday

• Thursday

Multiple Choice

How many students had more than 6 candy bars?

• 5
• 2
• 3
• 1

Multiple Choice

How many students scored 93% or less?

• 6
• 16
• 14
• 13

Multiple Choice

Students at Center Jr. High were surveyed and asked about their favorite school after work snack. The bar graph shows the results of the survey.

Based on the graph, which statement is true?

• Twice as many students chose ice cream as chose fruit for their favorite snack.

• Twice as many students chose chips/ dips as chose ice cream for their favorite snack.

• The same number of students chose chips/ dips as chose cheese & crackers as their favorite snack.

• Fifteen more students chose ice cream as chose cheese & crackers as their favorite snack.

Multiple Choice

Kim had a bag with colored marbles in it. The number of marbles in the bag is shown in the bar graph.

Which statement is NOT supported by the information in the graph?

• The bag contains more red and white marbles than blue and green.

• The ratio of red to blue marbles is 2:1.

• The ratio of blue to green marbles is 3:2.

• The ratio of red to green is 6.1.

Multiple Choice

Based on the graph, what percent of the books checked out was adventure or science fiction?

• 50%

• 62.5%

• 75%

• 80%

Multiple Choice

Answer the question pictured.

• A

• B

• C

• D

Multiple Choice

Answer the question pictured.

• A

• B

• C

• D

Mean, Median, Mode & Range

Mean, Median, Mode, and Range

M.Brines

What is Mean, Median, Mode, and Range?

• A mean in math is the average of a data set.

• The median is the middle number in a sorted list.

• Range in math is the difference between the highest and lowest value.

• Mode is the value that occurs most frequently in a given set of data.

Multiple Choice

What is mean, median, mode, and range?

• Mean is the average, median is the middle value, mode is the most frequent number, and range is the difference between the highest and lowest numbers.
• Mean is the sum of all numbers, median is the average, mode is the highest value, and range is the lowest value.
• Mean is the most frequent number, median is the difference between the highest and lowest numbers, mode is the middle value, and range is the average.
• Mean is the highest value, median is the lowest value, mode is the average, and range is the sum of all numbers.

Mean

As you have read before, Mean is the average number, or the number that is used the most, here are some examples on how to use Mean: Lets say you have some numbers 4, 12, 2, 1, 9, 7, 5, You would add all the numbers together, then you divide by the total of the number of numbers used.

Multiple Choice

How do you figure out the mean of a group of numbers?

• Add all numbers together, then divide by the total count of numbers.
• Subtract the largest number from the smallest number
• Multiply all numbers together
• Divide the total count of numbers by the sum of all numbers

Mode and Median

Median is the middle number, for example: 1,2,3,4,5,6,7,8,9; the median would be 5.

Median

Mode is the most numbers used, for example: 1,2,3,5,6,6,7; the mode would be 6.

Mode

Multiple Choice

What is an example of Mode?

Num: 1,2,4,4,4,5,6,7,8,8

• 2
• 5
• 4
• 9

Multiple Choice

How do you figure out the median in a group of numbers?

• Add all numbers and divide by the total count
• Select the highest number in the group and subtract it by the nearest whole

• Choose the first number in the list
• Put the numbers in order, then look for the middle number

Range

As you have read, range is the difference between the highest and lowest value. An example of range would be: 1,2,3,4,5,6,7,8,9, you would subtract the lowest number by the greatest number.

Fill in the Blank

What is the difference between the lowest and the greatest number?

Multiple Choice

Add up all the numbers in a data set and divide by the amount of numbers in the data set.

• Mean

• Median

• Mode

• Range

Multiple Choice

Subtract the smallest number in the data set from the biggest number in the data set.

• Mean

• Median

• Mode

• Range

Multiple Choice

Order the numbers in the data set from smallest to biggest and find the middle number in the data set.

• Mean

• Median

• Mode

• Range

Multiple Choice

Order the numbers in the data set from smallest to biggest and find the middle number in the data set.

• Mean

• Median

• Mode

• Range

Multiple Choice

The number that occurs the most in a data set.

• Mean

• Median

• Mode

• Range

Fill in the Blank

Find the Mean of the Data Set:

7, 8, 3, 4, 8

Median

To find the median, list the numbers in order from least to greatest and find the number in the middle.

If there are two middle numbers, add them together and divide by 2 to calculate the median.

Fill in the Blank

Find the Median in the Data Set:

7, 8, 3, 4, 8

Fill in the Blank

Find the Median of in the Data Set:

2, 9, 7, 4, 6, 1

Mode

Mode is the number that appears the most.

Fill in the Blank

Find the Mode in the Data Set:

7, 8, 3, 4, 8

Range

To find the range, list the numbers in order from list to greatest, then subtract the highest value from the lowest value.

Fill in the Blank

Find the Range in the Data Set:

7, 8, 3, 4, 8

Multiple Choice

Find the Mean, Median, Mode, and Range of the Data Set:

2, 10, 6, 8, 10, 4, 10, 4, 9

• Mean: 7 Median: 8 Mode: 10 Range: 12

• Mean: 7 Median: 8 Mode: 10 Range: 8

• Mean: 7 Median: 6 Mode: 4 Range: 8

• Mean: 7 Median: 8 Mode: 4 Range: 8

population

sample

inference

large

expensive

difficult

Multiple Choice

Pay close attention to highlighted text.

Which inference can be drawn based on the results?

• a

• b

• c

• d

Multiple Choice

Pay close attention to highlighted text. Compare to table shown.

Which statement is true?

• a

• b

• c

• d

Multiple Choice

What is a smaller, representative group drawn from a population?

• unit

• sample

• parameter

• statistic

Multiple Choice

The entire set of items (who or what) from which data can be selected

• survey

• parameter

• population

• sample

Vocabulary

• Population-- is an ENTIRE group of people or objects.

• Sample--is a PART of the population

• Example: NAMS is a population and the 7th grade students are a sample from the population.

Multiple Choice

A market research company wants to conduct a survey of voters to find out which candidate will likely win the next local elections.

Which sample population will give the most accurate data

• a random sample of supporters of one of the candidates

• a random sample of middle school kids

• a random sample of all voters in the district

• a random sample of visitors at a museum

Multiple Select

A bookstore owner asks every fifth customer on a single day if he or she owns an e-book reader. Select the random samples of the population from the list. Check all that apply.

• Store Customers

• Book Lovers

• People who buy books

• Book Store Owners

• E-book Owners

Multiple Choice

• The second half likely contains the higher scores so the graph will change.

• The second half likely contains the lower scores so the graph will change.

• The graph will likely balance out with each bar being the same height.

• The graph will probably look very similar to the way it appears now.

Multiple Choice

_______ is a part of a group being surveyed.

• Sample

• Population

• Random Sample

• Quartile

Multiple Choice

_______ is the entire group of objects or individuals considered for a survey.

• Sample

• Population

• Random Sample

• Quartile

Multiple Choice

Assign each car in a dealership a number and then use a random-number table to select the cars to be inspected. 

• systematic

• random sample

• convenience

• biased sampling

Multiple Choice

Leslie surveyed the 9 youngest students in the elementary school.  Is this sample of the students in the school likely to be representative of all the students in the school?

• yes

• no

Multiple Choice

Elise, a supermarket employee, approached 50 random customers and asked whether they would be willing to discuss what they like most about the store.  She interviewed the 22 who said yes.  Is this sample of the supermarket's customers likely to be biased?

• yes
• no

Lets try it!

A shipment to a warehouse consists of 3,500 MP3 players. The manager chooses a random sample of 50 MP3 players and finds that 3 are defective. How many MP3 players in the shipment are likely to be defective?

​

Fill in the Blank

A band has sold out a concert with 4,200 seats. A random sample of 120 ticket buyers is surveyed, and 28 buyers made their purchase on the first day tickets were being sold. How many of the 4,200 tickets are likely to have been purchased on the first day they were available?

A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the result of the survey.

Which inference about all freshmen at this college is best supported by this information?

F The number of freshmen who chose English as their major is less than

    the number of freshmen who are Undecided on their major.

G The number of freshmen who chose Education as their major is greater 

    than the number of freshmen who chose Science or Other as their major.

H The number of freshmen who chose Business or Education as their major

    is less than the number of freshmen who chose Science or Engineering 

    as their major.

J The number of freshmen who chose Business as their major is greater 

   than the number of freshmen who chose English as their major.

​

Making an inference using data from a table!

Multiple Choice

The manager of a music store surveyed a random sample of customers who shop in the store about their favorite type of music. The table shows the number of customers who selected each type of music.

Based on the information in the table, which inference about the favorite type of music of all the customers who shop in the music store appears to be valid?

• they are certain to select rock or pop music.

• They are less likely to select country or rap music than rock music.

• They are more likely to select country music than jazz, classical, or rap music.

• They are certain to select any type of music other than jazz music.

Multiple Choice

Valid inferences are based on data and are most likely true.

• TRUE

• FALSE

Multiple Choice

A ___ is the entire group of objects or individuals being studied.

• sample

• population

• random sample

• quartile

Multiple Choice

A ___ is a part of a group being surveyed.

• sample

• population

• random s

• quartile

Multiple Select

In order to collect good data, the sample needs to be unbiased.

To have an unbiased sample, it should be ___ and ___.

Select two answer choices.

• randomly selected

• rationalized through data

• representative of the population

• reflective of the needs of the survey

Multiple Choice

Several students were surveyed about their favorite drinks.

22 Fanta, 34 Pepsi, 20 Coke, and 29 Grape.

Predict how many students will like Coke if 500 students are surveyed?

• 158
• 60
• 142
• 95

Multiple Choice

Bob asked 8 band members and found that 3 members play more than one instrument.

Use his results to predict how many of Oak School's 152 band members play more than one instrument.

• 3/8
• 405
• 57
• 60

Multiple Choice

The TV station wants to get the opinion of viewers on the look of a new game-show set.  

The station's staff calls random people in the phone book.  Is this biased or unbiased?

• Biased
• Unbiased

Multiple Choice

The Candlelit-Dinner Candle Store surveys its Monday customers to find out their opinion on a new scented candle.  Is this biased or unbiased?

• Biased
• Unbiased

Multiple Choice

Lizzy had test scores of 72, 94, 108, 60.
What is the range of her test scores?

• 12
• 72
• 48
• 98

Multiple Choice

Find the mean of these numbers.
5, 11, 2, 12, 4, 2

• 4.1
• 6
• 4.5
• 4

random number

hat

bias

equal

random

Multiple Choice

_______ is a part of a group being surveyed.

• Sample
• Population
• Random Sample
• Quartile

Multiple Choice

_______ is the entire group of objects or individuals considered for a survey.

• Sample
• Population
• Random Sample
• Quartile

Multiple Choice

A sample in which every person, object, or event has an equal chance of being selected.

• A. Random sample.

• B. Biased sample.

Multiple Choice

Larger random sample sizes are more representative of a population.

• A. True

• B. False

Multiple Choice

When a sample does not accurately represent the population it is a:

• A. Unbiased sample

• B. Biased sample

Multiple Choice

A public library asked every 10th person who entered to name the type of book they were getting.

• A. Biased

• B. Not Biased

Multiple Choice

Fewer accidents occur at intersections with stoplights than at intersections that do not have stoplights. Would you be in favor of stoplights at the intersection of Main and Perry Streets?

• Biased

• Not Biased

Multiple Choice

To see who has a computer at home the front office chooses 10 students randomly per grade to ask

• Biased

• Not Biased

Multiple Choice

A senator wants to how she is doing. She sends a survey to 1000 registered voters in her party

• Biased

• Not Biased

Multiple Choice

Do you want a delicious salad for lunch or the usual sandwich?

• Biased

• Not Biased

Multiple Choice

Are you willing to deal with noise, heavy increases in traffic where you live just so another unnecessary mall can be built?

• Biased

• Not Biased

Multiple Choice

A group of people were asked about their favorite types of pants. Predict how many people out of 150 would say jeans are their favorite.

• 150

• 50

• 25

• 75

Multiple Choice

A group of people were asked about their favorite types of pants. Predict how many people out of 300 would say capris are their favorite.

• 300

• 90

• 15

• 50

Multiple Choice

A group was surveyed and asked about their favorite sport.  Predict how many people would chose football if there are 600 students in the school.

• 150

• 180

• 450

• 600

Multiple Choice

A group was surveyed and asked about their favorite sport.  Predict how many people would chose baseball/softball if there are 300 students in the school.

• 36

• 64

• 70

• 72

Multiple Choice

You did a survey and found out 65% of people like mustard on their hot dog. If there are 2,500 residents of a town, predict how many would say they like mustard on their hot dog.

• 65

• 1,625

• 2,000

• 2,500

Multiple Choice

A recent survey of 800 seventh graders from across the state shows 4 out of 10 like to play paper football. How many students said they like to play paper football?

• 40 students
• 200 students 
• 320 students
• 8,000 students

Multiple Choice

Darrien surveys 60 of the actors theater class. He concludes that 8 out of 15 actors have previous acting experience. How many actors would you expect to have experience out of 30?

• 8 actors
• 16%
• 8%
• 16 actors

Multiple Choice

Based on the results of the survey, Steven concludes that the favorite hobby of most students is watching movies.

Which statement best describes Steven's conclusion?

• a

• b

• c

• d

surveys

estimate

mean

number of values

Multiple Choice

Eight students were surveyed about the number of hours they spend reading for fun each week.

11, 4, 7, 13, 3, 7, 12, 5

What is the average number of hours spent reading for fun by the students each week?

• 7.75
• 9.25
• 8.0
• 6.5

Multiple Choice

Which statement best describes the mean of a data set?

• The average or the sum of all the values in the data set divided by the total number of data values in the set

• The difference between the highest and the lowest values in the data set

• The value that occurs most often in the data set

• The middle data value in the data set

Dropdown

To find the mean of a data set you have to ​

Select answer

all the values in the data set and ​

Select answer

by the total number of data values in the set.

Multiple Choice

At a farm there were 7 cows for every 2 horses. If there was 21 cows estimate how many horses there would be?

• 9

• 3

• 6

• 14

Multiple Choice

A jar contains 1,800 marbles. James enters a contest to guess the number of any one color of marbles in the jar. He is allowed to take 4 random samples of 200 marbles each. Approximately how many red marbles can he expect are in the jar?

• 500

• 525

• 550

• 600

Multiple Choice

To the nearest whole number, what is the best estimate for the squirrel population?

Are we looking for the "Part" or the "Whole?"

• a

• b

• c

• d

Multiple Choice

To the nearest whole number, what is the best estimate for the bee population?

Are we looking for the "Part" or the "Whole?"

• a

• b

• c

• d

Multiple Choice

What is the best estimate for the goat population in the countryside?

Are we looking for the "Part" or the "Whole?"

• a

• b

• c

• d

Multiple Choice

Which is a reasonable prediction of the mean height of all the ambrosia plants in the park?

• a

• b

• c

• d

Multiple Choice

What is the best estimate for the robin's population?

Are we looking for the "Part" or the "Whole?"

• a

• b

• c

• d

Multiple Choice

What is the best estimate for the robin's population?

Are we looking for the "Part" or the "Whole?"

• a

• b

• c

• d

Multiple

vary

variation

Multiple Choice

The double dot plot shows the number of city pet registrations for several days.

• The mean number of cat registrations is greater than the mean number of dog registrations.

• The dogs’ data has a mean of 10 registrations.

• The cats’ data has a mean of 15 registrations.

• The mean number of dog registrations is greater than the mean number of cat registrations.

Multiple Choice

The double box plot below shows the results of a school survey about types of lunch purchased.

• The a la carte data have less variation than full lunch.

• The a la carte data are centered around a higher value.

• The data for full lunch has a median of 180.

• The data for a la carte lunches has an interquartile range of 240 students.

Multiple Choice

The double box plot shows the number of Calories per serving for various fruits and vegetables.

• The median for the fruit data is 125.

• The median for the vegetable data is 75.

• The fruits have a higher number of calories with a greater variation.

• The vegetables have a higher number of calories with a greater variation.

Multiple Choice

The double dot plot shows the gas mileage, in miles per gallon, for several cars and SUVs.

• The cars have a greater gas mileage with a greater variation.

• The cars have a greater gas mileage with a less variation.

• SUVs have less gas mileage with greater variation.

• SUVs are centered around a greater median.

Multiple Choice

The double plot shows the daily attendance for two fitness clubs for one month.

• Fun Fit has greater attendance with greater variation.

• Greg's Gym has greater attendance with greater variation.

• Fun Fit has greater attendance with less variation.

• Greg’s Gym has a greater attendance with less variation.

Multiple Choice

The double box plot shows the heights in inches for the players on two professional basketball teams.

• While the median heights are about the same, the variation in heights is greater for the NJ Nets than the NY Knicks.

• While the median heights are about the same, the variation in heights is greater for the NY Knicks than the NJ Nets.

• The heights of the NJ Nets are more consistently centered around the median.

• The heights of the NY Knicks are less consistently centered around the median.

Multiple Choice

Ms. Andrey claims the average score on a quiz in her class was 25. Mr. Luna claims the average score on a quiz in his class is 25.

• Ms. Andrey used the mode, while Mr. Luna used the median.

• Ms. Andrey used the mean, while Mr. Luna used the mode.

• Both teachers used the mean.

• Both teachers used the median.

Multiple Choice

Reggie asked two classes about their favorite ice cream flavor. The results are shown in the table below.

Which statement is true?

• a

• b

• c

• d

Multiple Choice

Reggie asked two classes about their favorite ice cream flavor. The results are shown in the table below.

Which statement is true?

• a

• b

• c

• d

Multiple Choice

Lance surveyed his class to see how many students have pets. The results are shown in the table below.

Which statement is true?

• a

• b

• c

• d

Multiple Choice

A pet store company collected data from two random samples of customers regarding their preference of dog toy purchases.

Which statement can be made based on the data?

• a

• b

• c

• d

Multiple Choice

A survey of randomly selected college students was conducted to determine if the campus library should extend its hours of operation. The results of the survey are in the table.

If there are students at the college, what is the best estimate for the number of students who prefer the library to close at p.m.?

• a

• b

• c

• d

higher

lower

an error

more accurate

Multiple Choice

The front office of a baseball team surveyed two random population samples to determine whether there would be support to build a new baseball stadium.

Which conclusion is best supported by the survey results?

• a

• b

• c

• d

Multiple Choice

The students in the survey represent a population of 200. Which option best describes the population?

• a

• b

• c

• d

Multiple Choice

Eight hundred dentists were surveyed about the toothpaste they would recommend to their patients. The survey results are shown in the table below.

Dentists Survey Results

 ToothpasteNumber Recommended W280X165Y210Z145

Which of these could a commercial accurately state about the results of the survey?

• a

• b

• c

• d

Multiple Choice

Which statement about the bag of marbles is not supported by the data?

• a

• b

• c

• d