1

Unit 13 Statistics

COST OF MP3 PLAYERS

NAME:______________________

TEACHER:____________________

GRADE:______________________

50 55 60 65 70 75 80 85 90 95 100

Target

Best Buy

symmetric (mound-shaped) distribution Skewed Left

Skewed Right

2

Lesson 1 – Statistical Questions Classwork Day 1

Vocabulary

Statistical - ____________________________________________________________________________

Variability - ____________________________________________________________________________

There are two types of data: numerical and categorical. In a numerical data set, every value in the set is a

number. Categorical data sets can take on non-numerical values, such as names of colors, labels, etc. (e.g.,

“large,” “medium,” or “small”).

Example 1 For each of the following statistical questions, students asked Jerome to identify whether the data

are numerical or categorical. Explain your answer, and list four possible data values.

a. How old are the cards in the collection? b. How much did the cards in the collection cost?

c. Where did you get the cards?

A statistical question is one that can be answered by collecting data that vary (i.e., not all of the data values are

the same).

Think

Samantha wants to collect statistical information about the different sports seventh graders at her school like to

watch.

She writes 3 questions to ask 50 seventh graders and will use the results to make an estimate about all seventh

graders. Which questions are statistical and which are not?

When is the next home basketball game? Statistical or Not Statistical

What is your favorite sport to watch? Statistical or Not Statistical

What was the last sports game you watched at this school? Statistical or Not Statistical

When creating a statistical question we need to ask ourselves…

What are the possible answers to this question? Are the answers too general? Too Specific?

Explain in your own words the difference between a question that is statistical and one that is not.

____________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Conclude: If there is any variability (more than one answer) then it is statistical. If the answer is a fact (only

one answer) then it is non-statistical.

Try These

Determine whether each question is statistical or non-statistical. Then, explain your answer.

1. A political group asked voters waiting in line to vote: Who are the 2 major candidates running for president

this year?_____________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

WHAT IS YOUR

FAVORITE SPORT?

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Lesson 1 – Statistical Questions Classwork Day 1 2. The journalism club surveyed students in the library and asked: About how much time do you spend reading

each day?_____________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

_____________________________________________________________________________________

3. To decide if a new movie should be shown this Friday, a movie theatre invited 50 people to view the movie

and answer the question: Did you enjoy the movie? ___________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

More Practice

1. Write both a statistical and a non-statistical question you could ask some classmates to make a prediction

about teenagers and text messaging.

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

2. Which of the following questions has more variability?

A Did you play in the football game?

B What flavors of frozen yogurt does the yo-go mania offer?

Explain your answer ________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Talk through these problems as a class. Then write your answers below.

3. Compare. Which question is statistical and which is not? Explain how you know.

What is your favorite Olympic sport to watch?

When are the next Olympic games?

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Example 4. Indicate whether each of the following two questions is a statistical question.

Explain why or why not.

a. How much does Susan’s dog weigh?

b. How much do the dogs belonging to students at our school weigh?

5. If you collected data on the weights of dogs, would the data be numerical or categorical? Explain how you

know it is numerical or categorical.

4

STATISTICAL QUESTIONS CLASSWORK DAY 1

TRY THESE:

Example 1 For each of the following, determine whether the question is a statistical question. Give a reason for

your answer.

a. How many letters are in my last name?

b. How many letters are in the last names of the students in my 6th grade class?

c. What are the colors of the shoes worn by the students in my school?

d. What is the maximum number of feet that roller coasters drop during a ride?

e. What are the heart rates of the students in a 6th grade class?

f. How many hours of sleep per night do 6th graders usually get when they have school the next day?

g. How many miles per gallon do compact cars get?

Example 2 Identify each of the following data sets as categorical (C) or numerical (N). Explain your answer.

a. Arm spans of 𝟏𝟐 6th graders

b. Number of languages spoken by each of 𝟐𝟎 adults

c. Favorite sport of each person in a group of 𝟐𝟎 adults

d. Number of pets for each of 𝟒𝟎 3rd graders

e. Number of hours a week spent reading a book for a group of middle school students

3. The data shown are the responses to the question. How tall, in centimeters, is each bean plant? Make a dot

plot to display the data.

8 6 7 5 8 6 8 7 9 4

5 2 8 6 9 5 7 6 7 7

4. What statistical question might Brittany have asked to get this data?

18 min, 20 min, 30 min, 16 min, 45 min

A How long did you spend on homework last night?

B How long do the directions say to cook the pie?

C At what time does school end?

D How many minutes does it take Eric to get to school?

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LESSON 2- SAMPLING CLASSWORK DAY 2

IMPORTANT VOCABULARY:

Bias__________________________________________________________________________

Unbias___________________________________________________________________________________

Population: A whole group of people or objects Sample: A part of the group or population

Example: Example:

Sampling Methods:

Random Sample-___________________________________________________________________________

Systematic Sample-_________________________________________________________________________

Stratified Sample-__________________________________________________________________________

sampling variability – the chance variability that happens from one sample to another when repeated samples

are taken from the same population.

For each of the following, state which sampling method is being used:

1. 100 florists, chosen at random, are asked what their busiest season was: ____________________

2. 25 football players and 25 soccer players were asked which brand of sneaker they like: _____________

3. Every 10th customer at an auto shop was asked to evaluate the service: __________________________

4. 75 computer salespeople were asked, at random, which type of computer they sold most:_____________

5. 50 cat owners and 50 dog owners were asked what they liked most about owning a pet:_____________

6. Workers on an assembly line check every 10th tire: ___________________________

7. Names are drawn from a hat and selected to participate in a survey: _________________________

8. Students are surveyed in groups determined by grade level:_________________

9. Every tenth student from a list is selected to complete a survey:_________________

Biased Samples/Surveys:

Samples can be biased if they:

- Do not represent the entire population being surveyed -Are chosen based on convenience.

Ex: Ex:

-Involve only people who volunteer or want to be in the survey - A survey can also be biased if the questions

asked are leading questions.

Ex: Ex:

PASTA A grocery store asked every 20th person entering the store what kind of pasta they

preferred. The results are shown in the table. If the store decides to restock their shelves

with 450 boxes of pasta, how many boxes of lasagna should they order?

Not Fair

Pasta Number

Macaroni 38

Spaghetti 56

Rigatoni 12

Lasagna 44

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LESSON 2 - SAMPLING CLASSWORK DAY 2

1. A survey is conducted to compare the exercise habits of

students in Seneca. The results are noted in the chart

below:

[a] Is this survey biased? If so, why?

[b] How could this survey be more accurate?

Determine whether each of the following is BIASED or UNBIASED and explain:

2. A survey of teenagers that includes only teenage girls?

3. The survey question is: “Math is extremely important, what is the most important subject?”

4. A survey about favorite toys of 3 year olds that includes only 4 year olds

5. The survey question is: “What is your favorite movie?”

6. The survey question is: “People who don’t like The Hunger Games aren’t smart, what is your favorite

movie?”

7. Questioning every 8th person who enters the cafeteria to see if they like school lunch.

Consider this survey. Mr. Coffey wants to know how the students in his school feel about a new dress code.

He surveys all the students in his homeroom. Is his survey biased? If it is, what could he have done differently

to make it representative?

GRADE SAMPLE PERCENT

6TH 20 STUDENTS 20%

7TH 20 ATHLETES 60%

8TH 20 STUDENTS 20%

8. What is Mr. Coffey’s population?

9. What is Mr. Coffey’s sample?

10. Is Mr. Coffey’s sample biased?

11. What could he have done differently?

Discuss…What if Mr. Coffey arrives at school early one morning? He surveys

the first 50 students who arrive at school. Is this a good sample that is likely to

be representative? Explain

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LESSON 2 - SAMPLING CLASSWORK DAY 2

Match each of the following:

1. Population ______ A. Sampling method in which every individual or object in a

population has an equal chance of being selected.

2. Random Sample ______ B. Sampling method in which a population is divided into

subgroups that contain similar individuals or objects.

3. Sample ______ C. Whole group of people or objects.

4. Stratified Sample ______ D. Sampling method in which you select an individual and

then follow a pattern to select the others.

5. Systematic Sample ______ E. Part of a group.

Determine the Type of Sample:

6. Every fifth person who leaves a hospital is asked how the health care was. ____________________

7. 20 men and 20 women were asked what their favorite spot was to vacation. ___________________

8. From a list of 300 teachers who attend a conference, 50 teachers are chosen. ___________________

9. 40 names were drawn out of a hat, without looking, and asked to take a survey._________________

10. A sample is grouped by grade-level._______________

Determine whether each is BIASED or UNBIASED, explain:

11. “Do you agree with the basketball coach that basketball is the best sport?”

12. A survey about what 7th graders eat for lunch includes boys.

13. A survey about what 7th graders eat for lunch only includes boys.

14. “What book did you enjoy reading the most this year?”

15. A survey is conducted, but only the closest four people were surveyed.

16. A survey about favorite movies is conducted in a movie store.

17. A survey about favorite hobbies is conducted in a sports store.

18. A bookstore surveys every fifth customer about customer service.

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LESSON 2 - SAMPLING CLASSWORK DAY 2

19. A school store sells binders in four different colors. A survey is conducted by the staff of the store to find

the most popular color. The chart shows the results.

a. If a student from the survey is chosen at random, what is the probability that this

student chose red?

b. What percentage of the sample chose blue?

c. What percentage of the sample chose red?

d. If 450 binders are to be ordered to stock the school store, how many should be green?

e. Determine whether each of the following samples is biased or unbiased:

[1] Only boys are included.

[2] Every tenth student that walks into the school is surveyed.

[3] Students are selected at random through the use of a computer algorithm.

[4] Students are asked to volunteer to take the survey.

[5] Only Mr. Oakes’s first class was surveyed.

[6] Twenty-five girls and twenty-five boys were surveyed.

20. Suppose you want to find out the times of day teenagers listen to the radio. Determine whether each of

these samples is biased or unbiased:

a) Randomly surveying 100 listeners that are girls:_____________________

b) Randomly surveying 100 listeners that teenagers: _______________________

c) Surveying a group of boys and a group of girls, all of which are teenagers:_______________

d) Surveying only people listening to the radio at 4:00 in the afternoon:_____________

e) Surveying fifty 35 year old men and fifty 35 year old women:____________

f) Surveying only people who want to participate in the survey:____________

g) Randomly choosing 40 teenagers to participate:___________

Review

21. What is 5% of 600 22. What percent of 70 is 35?

23. An item costs $20 after a 20% discount was taken. What was the original price?

Color Number

Red 25

Green 10

Blue 13

Yellow 2

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Lesson 3 – Measures of Central Tendency Classwork Day 3

Important Vocabulary:

Measures of Central Tendency: _______________________________________________________________

Mean: ____________________________________________________________________________________

Mean (balance point) if you draw a dot plot of a set that it would balance at the mean.

Median:___________________________________________________________________________________

Mode: ____________________________________________________________________________________

Range: ___________________________________________________________________________________

Outlier: __________________________________________________________________________________

Given the following scores, what is the outlier or extreme value? 86, 82, 95, 32, 88

Inference______________________________________________________________

EXAMPLE: For the following set of data, find the mean, median, mode, and range. Make a dot plot to

illustrate the given data.

2, 3, 5, 5 , 5, 6, 7, 9, 11, 11

MEAN MEDIAN MODE RANGE

1 2 3 4 5 6 7 8 9 10 11

Find the mean, median, mode, and range using the data from the stem and leaf.

Stem Leaf Write the data on the line ___________________________________________

7 2 9

8 0 5 5

9 7

Measure of Central

Tendency

Most Useful When…

MEAN

MEDIAN

MODE

[1] Which central tendency (mean, median or mode) would be best to use with the following data:

a) 90, 92, 88, 95, 30, 91 b) 3, 3, 6, 3, 4, 3, 3, 5 c) 95, 92, 93, 94, 90, 95

d) 30, 29, 31, 30, 30, 30 e) 91, 89, 92, 90, 88, 93 f) 80, 82, 85, 88, 61, 87

g) 120, 117, 119, 21, 122 h) 91, 91, 91, 90, 91, 97 i) 75, 77, 72, 73, 78, 79

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Lesson 3 – Measures of Central Tendency Classwork Day 3 [2] Christopher would like to have an average of 96 in his math class. So far, he has scored a 98, 98, 94, and

100. What is the lowest grade Christopher can get to maintain a 96 average?

[3] Jill needs an average score of 92 on five quizzes to earn an ‘A’. The mean of her first four scores was 91.

What is the lowest score that she can receive on the fifth quiz to earn an A (92)?

[4] Justin had an average of 97 on his first 4 tests. After his fifth test, his average dropped to 95. What was his

score on the fifth test?

Example 5 Imagine you are balancing pennies on a ruler. Suppose you place one penny each at 3, 7, and 8

on a ruler.

a. Sketch a picture of the ruler. At what value do you think the ruler will balance? Mark the

balancing point with the symbol ∆.

b. What is the mean of 𝟑, 𝟕, and 𝟖? Does your ruler balance at the mean?

c. Show part (a) on a dot plot. Mark the balancing point with the symbol Δ.

d. What are the deviations from each of the data points to the balancing point? What is the sum of the

deviations? What is the value of the mean?

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Measures of Central Tendency Classwork Day 3

FIND THE MEAN, MEDIAN, MODE, AND RANGE FOR EACH SET OF DATA. ROUND TO THE NEAREST TENTH, IF

NECESSARY.

1) MIKE’S TEST SCORES: MEAN:_______ MEDIAN:________ MODE:________ RANGE:________

Stem Leaf

5 0 Write the scores on this line: _50, 74,_______________________________________

6

7 4 8

8 2 4

9 0 0

10 0

2) INCHES OF RAIN: 4, 6, 12, 5, 8

MEAN:_______

MEDIAN:________

MODE:________

RANGE:________

3) ANNUAL INCHES OF SNOW:

X

X X X X

X X X X X X X

MEAN:______

MEDIAN:________

MODE:________

RANGE:________

4) Dominic would like to have an average of 85 in his math class. So far, he has scored a 78, 92, 80, and 82.

What is the lowest grade Dominic can get to maintain a 85 average? (set up the equation)

Review

5) A pair of socks went from $5 to $6, what is the percentage change?

6) Simplify 2( 3x + 5) - 3

1(6x + 18) 7) Subtract nmfromnm 25.43

2

1

5 6 7 8 9

4

4

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Lesson 3 – Measures of Central Tendency Classwork Day 3

8) The ages of five children in a family are 3, 3, 5, 8, and 18. Which statement is true for this group of data?

a) median = mode b) median > mean

c) mean > median d) mode > mean

9) A shoe store owner is looking at a bar graph that shows the different styles of shoes he sold over the past 6

months. Which of the following measures would indicate the most popular style?

a) mode b) median

c) mean d) range

10) The temperature in Alaska was recorded every 4 hours over the course of a day. The results are shown

below:

[a] What is the range of this data?

[b] What was the average temperature in Alaska for this day?

Example 11 Listed are four statistical questions and four different dot plots of data collected to answer the

below questions. Match each statistical question with the appropriate dot plot. Explain each of your choices.

Statistical Question:

a) What are the ages of 4th graders in our school?

b) What are the heights of the players on the 8th grade boys’ basketball team?

c) How many hours do 6th graders in our class watch TV on a school night?

d) How many different languages do students in our school speak?

Time Temp

12:00 am -12°

4:00 am -2°

8:00 am 4°

12:00 pm 7°

4:00 pm 8°

8:00 pm 2°

Plot A Plot B

Plot C Plot D

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Lesson 4 - Mean Absolute Deviation MAD Classwork Day 4

Vocabulary

Outlier/Extreme Value - __________________________________________________________________

Mean - _________________________________________________________________________________

Absolute Value - _________________________________________________________________________

Deviate - ________________________________________________________________________________

Absolute Deviation = absolute value of the deviation

Mean Absolute Deviation (MAD) It tells you how the data is spread out compared to the mean.

Variability -

Mean (average) absolute deviation (MAD) is calculated by taking the mean of the absolute deviations for

each data point. We do not use this method of describing data when there is an outlier or extreme value.

Vary – to differ

Ex) the houses vary in size

Measures of variation is similar to measures of central tendency (mean, median, and mode) because it helps us

describe the data. Measures of central tendency help us describe the center of a set of data. Measures of

variation show how close together the data in a set are or how far apart data points are.

How do you calculate mean absolute deviation?

Step 1 – calculate the mean of the data.

Step 2 – subtract the mean and each data point.

Step 3 – take the absolute value (distance is always positive)

How far away from the mean are you? Ex. Mean = 10 #12?______

Step 4 – Take the average of the absolute deviations.

Guided Practice Ex #1: Plant Heights: 18, 27, 21

Mean: 22

Data

x

Mean

x

Calculate the Deviation

xx

Absolute deviation

18 22 2218 4

27

21

Mean Absolute Deviation =

Conclusion: The plant heights vary by an average of ________________inches from the mean.

Mean

Height

If the MAD is small, it means the data

are bunched closely together. If the

MAD is large, it means the data are

spread out and have greater variability.

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Lesson 4 - Mean Absolute Deviation MAD Classwork Day 4

Ex #2: Data: 5, 6, 7, 9, 10, 12, 20

Mean: 9.86 (rounded to the nearest hundredth)

Data Mean

x

Calculate the Deviation

xx

Absolute deviation

5 9.86 86.95 4.86

6 9.86 3.86

7 9.86

9 9.86

10 9.86

12 9.86

20 9.86

Find the mean absolute deviation. Round to the nearest tenth. Show work

Mean Absolute Deviation = 3.551428…… ( 24.86 divided by 7) answer: 3.6

Ex #3: Data: 10, 20, 30, 1000, 1500

Mean: 512

Data Mean

x

Calculate the Deviation

xx

Absolute deviation

10 502

20 492

30

1000

1500

Find the mean absolute deviation.

Mean Absolute Deviation = 590.4 (2952 divided by 5)

How do the two data sets compare in examples 2 and 3? Explain what you know and how you know it.

Multiple Choice Practice

4. The following data are given: 12, 9, 16, 23, 30, 9, 6, 15, 18, and 23. Which of the following shows the

mean and MAD for these data?

A. Mean = 16.1, and MAD = 16.1 B. Mean = 16.1, and MAD = 5.92

C. Mean = 5.92, and MAD = 5.92 D. Mean = 5.92 and MAD = 16.1

5. Look at the table to the right.

Which statement CANNOT be made about these data?

A On a dot plot, Team A will be farther to the right, and the dots will be spread out.

B On a dot plot, Team B will be farther to the left, and the dots will be clustered.

C The mean for Team A was determined from more scores than the mean for Team B.

Mean MAD

Team A 18.6 4

Team B 12 1

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Lesson 4 - Mean Absolute Deviation MAD Classwork Day 4

1. Rachel and Molly are in the same reading class. Rachel’s scores on her first three vocabulary quizzes were

79, 86, and 90. Molly’s scores were 70, 78, and 80. Calculate the means and the mean absolute deviations of

their quiz scores. Compare them.

step 1: Calculate the MAD for Rachel’s scores Step 2: Calculate the MAD for Molly’s scores

DATA

POINT,

x

MEAN ABSOLUTE

DEVIATION

FROM MEAN

xx

ABSOLUTE

DEVIATION

Whose scores deviated more from the mean? Rachel or Molly Explain________________________

____________________________________________________________________________________

Review

2) Below is the data collected from two random samples of 100 students regarding student’s school lunch

preference.

Make at least two inferences based on the results.

1.

2.

Example 3 Match the following sets of summary measures with the corresponding dot plot. Only ONE dot plot

matches each group of summary measures. Explain why you selected the dot plot or why the other dot plots

would not represent the summary measures. Note: the same scale is used in each dot plot.

Next Page

Lesson 4 - Mean Absolute Deviation MAD Classwork Day 4

Student Sample Hamburgers Tacos Pizza Total

#1 12 14 74 100

#2 12 11 77 100

DATA

POINT,

x

MEAN ABSOLUTE

DEVIATION FROM

MEAN

xx

ABSOLUTE

DEVIATION

a. Median = 𝟖 and IQR = 𝟑 Plot # ________

b. Mean = 𝟗.𝟔 and MAD = 𝟏.𝟐𝟖 Plot # _______

c. Median = 𝟔 and Range = 𝟓 Plot # ________

16

Jason wanted to compare the mean height of the players on his favorite basketball and soccer teams. He thinks

the mean height of the players on the basketball team will be greater but doesn’t know how much greater. He

also wonders if the variability of heights of the athletes is related to the sport they play. He thinks that there will

be a greater variability in the heights of soccer players as compared to basketball players. He used the rosters

and player statistics from the team websites to generate the following lists. Was he correct? Explain

Basketball Team – Height of Players in inches for 2010 Season

75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84, 82, 84, 80, 84

Soccer Team – Height of Players in inches for 2010

73, 73, 73, 72, 69, 76, 72, 73, 74, 70, 65, 71, 74, 76, 70, 72, 71, 74, 71, 74, 73, 67, 70, 72, 69, 78, 73, 76, 69

To compare the data sets, Jason creates a two dot plots on the same scale. The shortest player is 65 inches and

the tallest players are 84 inches.

Basketball Team

Soccer Team

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

17

Lesson 5 – Variability – Box plot Classwork Day 5

Important Vocabulary:

Variability:________________________________________________________________________________

Remember the more choices (answers to a question) or the more numbers are spread out from the mean, the

more variability.

Box Plot:________________________________________________________________________________

________________________________________________________________________________________

Interquartile Range (IQR)___________________________________________________________________

__________________________________________________________________________________________

Mean Absolute Deviation (MAD)____________________________________________________________

Remember: Median is paired with the interquartile range and mean is paired with the mean absolute

deviation .

Guided Instruction - Box-Plots: Use the shown box-plot to answer the questions:

What is the least value?

What is the lower quartile?

What is the median?

What is the upper quartile?

What is the greatest value?

What is the range?

What is the interquartile range (IQR)?

Practice:

1. What is the least value?

2. What is the upper quartile?

3. What is the median?

4. What is the range?

5. What is the greatest value?

6. What is the lower quartile?

7. What is the interquartile range?

0 1 2 3 4 5 6

8 9 10 11 12 13 14

18

Lesson 5 – Variability – Box plot Classwork Day 5

8. Construct a box plot to represent the following data. Be sure to label the minimum, maximum, median, upper

quartile, and lower quartile. 12, 11, 9, 18, 10, 11, 7, 16, 14, 11, 6

Step 1: Order the #’s from least to greatest on the line below:

_______________________________________________________

Step 2: Find the median of the numbers listed in step 1 and circle/list it. Next, put brackets around the numbers

to the right and numbers to the left.

Step 3: Find the median of scores to the left and right of the median. (circle them)

Step 4: List all the important information to display the data on a box and whiskers.

Minimum ________

Maximum________

Median __________

Lower Quartile ________

Upper Quartile ________

a. What is the least value? b. What is the lower quartile? c. What is the median?

d. What is the upper quartile? e. What is the greatest value? f. What is the range?

g. What is the interquartile range?

Patrons in the children’s section of a local branch library were randomly selected and asked their ages. The

librarian wants to use the data to infer the ages of all patrons of the children’s section so he can select age

appropriate activities. In questions 11-13, complete each inference.

7, 4, 7, 5, 4, 10, 11, 6, 7, 4

9. Make a box plot (box and whiskers) of the sample population data

Minimum ________

Maximum________

Median __________

Lower Quartile ________

Upper Quartile ________

Example 10 On the graph below, insert the following words in approximately the correct position.

Maximum Minimum IQR Median Lower Quartile (Q1) Upper Quartile (Q3)

2. Estimate the IQR based on the data set above.

19

Lesson 5 – Variability Classwork Day 5

TRY THESE:

1. What is the least value? 2. What is the lower quartile?

3. What is the median? 4. What is the upper quartile?

5. What is the greatest value? 6. What is the range? 7. What is the interquartile range?

8. Construct a box plot for the following scores: 3, 5, 9, 8, 4, 7

Minimum ________

Maximum________

Median __________

Lower Quartile ________

Upper Quartile ________

9. Find the MAD of each dot plot. Create a table to show work.

Race Times (min)

9. Finding the Mean Absolute Deviation (MAD): Inches of Rain in the Last Eleven Days

Remember the steps: Draw a table to help you.

Step 1: Find the mean of the data

Step 2: Find the absolute value of the differences

between each value and the mean.

Step 3: Find the average of the mean deviations.(MAD)

Make a table to help you.

0 10 20 30 40 50 60

13 14 15 16 17 18 19

13 14 15 16 17 18 19

John

Stephen

0 1 2 3 4 5 6

Based on the data above, which runner do

you think runs at a more consistent pace?

Explain.

Is their overlap? Yes or No If so, describe

the overlap of the above data.

20

Lesson 5 – Variability Classwork Day 5

Example 10 Molly presented the plots below to argue that using a dial up connection would be better than

using a broadband connection. She argued that the dial up connection seems to have less variability around the

median even though the overall range seems to be about the same for the download times using broadband.

What would you say?

Example 11 Data on average rainfall for each of the twelve months of the year were used to construct the two

dot plots below.

a. How many data points are in each dot plot? What does each data point represent?

b. Make a conjecture about which city has the most variability in the average monthly amount of precipitation

and how this would be reflected in the IQRs for the data from both cities.

c. Based on the dot plots, what are the approximate values of the interquartile ranges (IQR) of the amount of

average monthly precipitation in inches for each city? Use each IQR to compare the cities.

d. In an earlier lesson, the average monthly temperatures were rounded to the nearest degree Fahrenheit. Would

it make sense to round the amount of precipitation to the nearest inch? Why or why not?

e. Make a box plot of the amount of precipitation for each city.

21

Lesson 6– Variability mixed practice Classwork Day 6

VOCABULARY

SYMMETRICAL _________________________________________________________________

DRAW A LINE(S) OF SYMMETRY FOR THE FOLLOWING FIGURES.

Symmetry of Box-Plots: Which is symmetrical? Write the percent on the line.

A B

Which plot has more variability, A or B? ______ Explain _______________________________________

______________________________________________________________________________________

Looking at set A what percent of data is at least 2? ________________________

COMPARING TWO POPULATIONS:

Examples:

Samantha surveyed a different group of students in her science and math classes. The double box plot shows

the results for both classes. Compare their centers and variations. Write 4 inferences you can draw about the

two populations.

NUMBER OF TV SHOWS WATCHED THIS WEEK

Is there overlap? yes or no If so, please describe the overlap?

0 1 2 3 4 5 6 0 1 2 3 4 5 6

0 5 10 15 20 25 30

Science Class

Math Class

Inference 1:

Inference 2:

Inference 3:

Inference 4:

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Lesson 6– Variability mixed practice Classwork Day 6

1. The double box plot shows the costs of MP3 players at two different stores. Compare the centers and

variations of the two populations. Write at least 3 inferences you can draw about the two populations.

COST OF MP3 PLAYERS

Is there overlap? yes or no If so, describe the overlap.

2. The double dot plot below shows the daily high temperatures for two cities for thirteen days. Compare the

centers and variations of the two populations. Write 2 inferences you can draw about the two populations.

DAILY HIGH TEMPERATURES

Inference 1__________________________________________________________________________

Inference 2 __________________________________________________________________________

50 55 60 65 70 75 80 85 90 95 100

Target

Best Buy

78 79 80 81 82 83 84 85 86 87 88

78 79 80 81 82 83 84 85 86 87 88

Inference #1 ______________________________________________________________________________________

Inference #2 ______________________________________________________________________________________

Inference #3 ______________________________________________________________________________________

City 1

City 2

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Lesson 6– Variability mixed practice Classwork Day 6

1. The double box plot shows the daily participants for two zip line companies for one month. Compare the

centers and variations of the two populations. Which company has the greatest number of daily participants?

NUMBER OF DAILY PARTICIPANTS

a) Which zip line company has more variability? Explain ______________________________________

_______________________________________________________________________________________

b) Is there overlap? yes or no If so describe the overlap.

c) Make at least 2 inferences based on the box plots.

Inference #1

____________________________________________________________________________________

Inference #2

____________________________________________________________________________________

Inference #3

____________________________________________________________________________________

2. The double dot plot shows the number of new emails in each of Mike’s and Hannah’s inboxes for 16 days.

NUMBER OF EMAILS IN INBOX - MIKE

NUMBER OF EMAILS IN INBOX - HANNAH

Compare the centers and variations of the two populations. Write an inference you can draw about the two

populations.

20 30 40 50 60 70 80 90 100 110 120

Zip Adventures

Treetop Tours

28 29 30 31 32 33 34 35 36 37 38

28 29 30 31 32 33 34 35 36 37 38

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Lesson 6– Variability mixed practice Classwork Day 6

The dot plots compare the number of raffle tickets sold by boys and girls during

a school fundraiser.

1. Which plot has an outlier?

A Girls B Boys C both plots D neither plot

2. What is the difference between the medians for the two data sets?

A 0 tickets B 2 tickets C 4 tickets D 6 tickets

Use the box plots for 3 and 4.

3. What is the interquartile range for the Checkers Club?

A 4 B 5 C 10 D 11

4. Which data set shows a greater spread?

A Chess Club B Checkers Club C They have the same spread. D You cannot tell from the box plots.

Use the dot plots for 5–7.

The dot plots show the number of hours students in two classes studied.

5. What percent of each class studied less than 4 hours? 6. Find the medians.

Math: ____________ Science: __________ Math: ____________ Science: __________

7. Compare the centers and spreads.

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Histograms Classwork Day 7

Vocabulary

Intervals - __________________________________________________________________________

Frequency - _________________________________________________________________________

Cumulative Frequency - _______________________________________________________________

Data from a frequency table can be displayed as a histogram. A histogram is a type of bar graph used to display

numerical data that have been organized into equal intervals.

Answer the following question using the histograms below:

1) How many students scored at least an 81 on the test? 5) How many movies grossed at least $141

million?

2) How many students scored less than and 81 on the 6) How many movies grossed between $61

million and

exam? $180 million?

3) Can you determine the highest grade from the 7) Can you determine how many movies grossed

Histogram? Explain. between $121 and $140 million?

4) How many students received a grade of 51? 8) How many movies grossed $260

million?

Exam Scores

0

2

4

6

8

10

12

14

51-

60

61-

70

71-

80

81-

90

91-

100

Score

Nu

mb

er

of

Stu

de

nts

Exam Scores

0

2

4

6

8

10

12

14

61-

100

101-

140

141-

180

181-

220

221-

260

Score

Nu

mb

er

of

Stu

den

ts

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Histograms Classwork Day 7

9) Construct a cumulative frequency table for the age of students who read Garfield:

8, 12, 16, 20, 22, 15, 7, 8, 11, 13, 14, 9, 14, 8, 10, 21, 18, 11, 13, 9

Age Group in intervals Tally Frequency Cumulative Frequency

5-9

10-14

15-19

20-24

10) Construct a cumulative frequency table for the age of students in a college night course:

26, 36, 34, 40, 38, 31, 21, 23, 20, 22, 24, 31 29, 24, 29, 40, 28, 39, 32, 35

Use the Intervals of 20-24, 25-29, 30-34, 35-40

Age Group in intervals Tally Frequency Cumulative Frequency

20-24

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Calculators are allowed for completing your problems.

Example 11 Hector’s mom had a rummage sale, and after she sold an item, she tallied for how much money she

sold the item. Following is the frequency table Hector’s mom created:

a. What was the total number of items sold at the rummage sale?

b. Complete the relative frequency column. Round to the nearest thousandth.

c. What percent of the items Hector’s mom sold was sold for $15 or more, but less than $20?

Example 12 Below is a relative frequency histogram of the maximum drop (in feet) of a selected group of roller

coasters.

a. Describe the shape of the relative frequency histogram.

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STUDY GUIDE - HOMEWORK HELP!!!!!

The double dot plot shows the height in inches for the girls and boys in Franklin’s math class. Compare the

centers and variations of the two populations. Round to the nearest tenth. Write an inference you can draw

about the two populations.

Girls

Remember…

Both Symmetrical Mean and MAD (Mean Absolute Deviation)

*Overall, the girls’ heights are lower than the boys’ heights. Girl’s Mean(65) < Boy’s Mean(69)

*The girls’ heights are more consistently grouped together than the boys’ heights. Girls’ MAD(0.8 )< Boys’ MAD(1.4)

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