1 6th Grade Statistical Variability 20151103 www.njctl.org 2 - - PowerPoint PPT Presentation

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6th Grade

Statistical Variability

2015­11­03 www.njctl.org

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Table of Contents

Measures of Center Central Tendency Application Problems

Click on a topic to go to that section.

Measures of Variation Mean Median Mode Minimum/Maximum Range Quartiles Outliers Mean Absolute Deviation Glossary What is Statistics? Teacher Notes

Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end

• f the presentation with the

word defined on it.

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What is Statistics?

Return to Table of Contents Teacher Notes This is the first time most of this unit's content will be presented to the students. So, this section is an introduction to statistics, and is meant to serve as a unit

• pener.

It briefly defines and describes the use and purpose of statistics.

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Everyday we encounter numbers. We use numbers throughout the day without even realizing it. What time did each of us wake up? How many minutes did we have to get ready? How far from school do we live? How many students will be in class today? How long is each class? And so on...

Data

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This information comes at us in the form of numbers, and this information is called data. If we start trying to put together all of this data and make sense of it, we can get overwhelmed. Statistics is what helps us along.

Statistics is the study of data.

Data

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Lets put statistics to work! Two 6th grade math classes took the same end of unit test. Here are their results. What conclusions can you draw by looking at the numbers?

Class 1: 89, 88, 92, 78, 85, 89, 95, 71, 100, 88, 97, 82, 77, 98, 86, 82, 95, 88 Class 2: 100, 53, 92, 91, 97, 93, 92 Data Conclusions

Math Practice

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When we just look at a list of numbers, it can take a lot of time to make sense

• f what we are dealing with.

Let's use Statistics to analyze the two classes scores. A good way to compare them is to start with their averages.

Statistics

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Class 1: 89, 88, 92, 78, 85, 89, 95, 71, 100, 88, 97, 82, 77, 98, 86, 82, 95, 88 Class 2: 100, 53, 92, 91, 97, 93, 92

Class 1 average: 88 Class 2 average: 88 So if we spread out the total points scored in each class, to give each student the same score, each student in both classes will have an 88. So can we assume that both classes had similar scores on the test?

Statistics Example

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Lets graph the results and have another look. The red line on the graph marks the class average. Discuss the following questions with your group.

• 1. How does the number of students in each class affect the scores?
• 2. How do the student scores compare to the average in each class?
• 3. Is the average a fair way to compare the two classes scores?

Why or why not?

Graphing Statistics

Math Practice

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The average is one way to analyze data, but it is not always the best way. Sometimes there are other factors to consider. Such as:

• The number of values in a data set.
• The difference between the highest and lowest value. (Range)
• If there are any values that are far apart from the rest. (Outliers)
• How the values compare to the average or mean. (Mean Deviation)

Statistics

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Lets use these statistical tools to compare the classes results.

• # of values in each data set
• Class 1 had 18 students, while class 2 only had 7. So the one poor

score from class 2 had a significant impact on the class average.

Statistics Example

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• Range
• Class 2 has a much larger range than class 1. This shows that the

scores were more spread out / farther apart, than class 1.

Range: 29 Range: 47

Statistics Range

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• Outliers
• The scores have been ordered to make it easier to see any outliers.

As you can see, in class 1 the scores flow nicely from least to greatest. However, in class 2, the score 53 is much lower than the rest of the scores. The large range in class 2 was due to the score of 53. If we eliminate that score, the range is only 9.

Statistics Outliers

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• Mean Deviation
• Every score in class 1 was within 17 points of the mean.
• In class 2, the score of 53 was 35 points from the mean. If that
• utlier was eliminated, the mean would be 94 and would more

accurately reflect the majority of the students' scores.

Statistics Mean Deviation

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After looking more closely at the data, what conclusions can we draw? Discuss the following question with your group.

Statistics Example

Math Practice

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1 Statistics is the study of data. True False

Answer

True

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2 Data is a collection of facts, values or measurements True False

Answer

True

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3 The purpose of statistics is to: (Select all that apply) A Collect numerical information B Organize numerical data C Analyze numerical information D Interpret numerical data

Answer

A, B, C, D

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A statistical question is a question that creates a variety of answers. Depending on the question, the data gathered can be numerical (hours spent studying) or categorical (favorite food). Our focus is on questions that create numerical data. Statistical Question Non­Statistical How many cupcakes of each type were made by the bakery last week? How many cupcakes were made by the bakery last week? How many cupcakes did each person in my class eat last week? How many cupcakes did I eat last week?

Statistical Questions

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4 Which statistical question best fits the data graphed below? A How many glasses of milk does each member of

• ur class drink a day?

B How many letters are in the last name of each class member? C How many text messages did each class member send last week? D How many minutes did each class member spend doing homework last night?

Answer

A

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5 Which statistical question best fits the data graphed below? A How many movies did each member of the class watch last night? B How many books did each member of the class bring home last night? C How many pencils does each member of the class have in his or her desk? D How many feet high is each member of the class?

Answer

C

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6 Which question is a statistical question? A How tall is the oak tree? B How much did the tree grow in one year? C What are the heights of the oak trees in the schoolyard? D What is the difference in height between the oak tree and the pine tree?

From PARCC EOY sample test non­calculator #12

Answer

C

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This was just a small look at statistics in action. Throughout this unit, you will learn many statistical tools that you can use to analyze and make sense of data. Think of it as a statistical toolbox. It is not just important to know how to use the tool, but what jobs to use the tool for. For example, you wouldn't use a hammer to staple your papers together.

Statistical Toolbox

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Measures of Center

Return to Table of Contents

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Activity

Each of your group members will draw a color card. Each person will take all the tiles of their color from the bag. Discussion Questions

• How many tiles does your group have in total?
• How can you equally share all the tiles? How many would each

member receive? (Ignore the color)

• Each member has a different number of tiles according to color.

Write out a list of how many tiles each person has from least to

• greatest. Look at the two middle numbers. What number is in

between these two numbers?

Math Practice

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Follow­Up Discussion

What is the significance of the number you found when you shared the tiles equally? This number is called the mean (or average). It tells us that if you evenly distributed the tiles, each person would receive that number. What is the significance of the number you found that shows two members with more tiles and two with less? This number is called the median. It is in the middle of the all the numbers. This number shows that no matter what each person received, half the group had more than that number and the other half had less.

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Vocabulary

Measures of Center:

• Mean ­ The sum of the data values divided by the number
• f items; average
• Mode ­ The data value that occurs the most often
• Median ­ The middle data value when the values are written

in numerical order

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Finding the Mean To find the mean of the ages for the Apollo pilots given below, add their ages. Then divide by 7, the number of pilots. Apollo Mission

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12 13 14 15 16 17

Pilot's age

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37 36 40 41 36 37

Mean Example

Answer

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Find the mean 10, 8, 9, 8, 5

Mean Practice

Answer

8

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7 Find the mean 20, 25, 25, 20, 25

Answer

23

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8 Find the mean 14, 17, 9, 2, 4,10, 5, 3

Answer

8

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Given the following set of data, what is the median? 10, 7, 9, 3, 5 What do we do when finding the median of an even set of numbers?

Median Practice

Answer & Math Practice

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When finding the median of an even set of numbers, you must take the mean of the two middle numbers. Find the median 12, 14, 8, 4, 9, 3

Median Practice

Answer

8.5

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9 Find the median: 5, 9, 2, 6, 10, 4 A 5 B 5.5 C 6 D 7.5

Answer

B

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10 Find the median: 15, 19, 12, 6, 100, 40, 50 A 15 B 12 C 19 D 6

Answer

C

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11 Find the median: 1, 2, 3, 4, 5, 6 A 3 & 4 B 3 C 4 D 3.5

Answer

D

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12 What number can be added to the data set below so that the median is 134? 54, 156, 134, 79, 139, 163

Answer

Any number less than

• r equal to 133

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13 What number can be added to the data set below so that the median is 16.5? 17, 9, 4, 16, 29,

Answer

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What do the mean and median tell us about the data?

• Mr. Smith organized a scavenger hunt for his students. They had to

find all the buried "treasure". The following data shows how many coins each student found. 10, 7, 3, 8, 2 Find the mean and median of the data. What does the mean and median tell us about the data?

Mean, Median, and Data

Teacher Notes The mean is 6 and the median is 7. The mean tells us that if the data were evenly distributed, each student would have 6 coins. The median tells us that half the class has more than 7 coins and the other half has less than 7.

41

Find the mode 10, 8, 9, 8, 5 Find the mode 1, 2, 3, 4, 5 What can be added to the set of data above, so that there are two modes? Three modes?

Mode Practice

Answer & Math Practice

MP8 ­ Look for and express regularity in repeated reasoning Ask: ­What do we now about the mode that we can apply to this new situation? ­How is this new situation similar to finding the mode in the first place? Different?

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14 What number(s) can be added to the data set so that there are 2 modes: 3, 5, 7, 9, 11, 13, 15 ? A 3 B 6 C 8 D 9 E 10

Answer

A & D

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15 What value(s) must be eliminated so the data set has 1 mode: 2, 2, 3, 3, 5, 6 ?

Answer

2 or 3

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16 Find the mode(s): 3, 4, 4, 5, 5, 6, 7, 8, 9 A 4 B 5 C 9 D No mode

Answer

A & B

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17 What number can be added to the data set below so that the mode is 7? 5, 3, 4, 4, 6, 9, 7, 7

Answer

46

Central Tendency Application Problems

Return to Table of Contents

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Teachers: Use this Mathematical Practice Pull Tab to compliment slides 48­51.

Teacher Notes & Math Practice

48

Which Measure of Center to Use?

Find the mean, median and mode and compare them. Sherman and his friends had a paper competition. The distances each plane traveled were 13 ft, 2 ft, 19 ft, 18 ft and 16 ft. Should Sherman use the mean, median or mode to describe their results?

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Mean: Median: Mode: 13.6 ft 16 ft no mode

Click for answer Click for answer Click for answer

Which measure of center best describes the data? The median is closest to most of the values, so it best describes the data. 13 ft, 2 ft, 19 ft, 18 ft and 16 ft The mean is less than 3 out of the 5 values, and there was no mode.

Click for answer

Which Measure of Center to Use?

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Foodie grocery store sells several juice brands in 12 oz bottles. Which measure of center best describes the cost for a 12 oz bottle of juice?

Using Measures of Center to Describe Data

Brand A $1.25 Brand D $0.99 Brand B $0.95 Brand E $1.99 Brand C $1.09 Brand F $0.99

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Mode: $0.99 Half of the data is greater than the median, and half of the data is less than the median. The Mean is greater than most of the data. The mode reflects the lower 4 values very well, but is much lower than the top two values. Mean: $1.21 Median: $1.04 In order to see how the measures

• f center compare to the data, the

data needs to be in order from least to greatest. The data has been graphed to help you see the comparisons.

Measures of Center Data

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18 Which measure of center best describes the data set? 2, 2, 2, 4, 4, 7, 7, 7 A mean B median C mode

Answer

B

53

19 Sarah records the number of texts she receives each

• day. During one week, she receives 7, 3, 10, 5, 5, 6, and

6 texts. Which measure of center best describes this data? A mean B median C mode

Answer

A

54

20 Thomas Middle School held a track meet. The times for the 200­meter dash, in seconds, were 22.3, 22.4, 23.3, 24.5 and 22.5. Does the mean, median or mode best describe the runners' times? A mean B median C mode

Answer

A

55

21 Julie is comparing prices for a new pair of shoes. The prices at seven different stores are $18.99, $17.99, $19.99, $17.99, $17.99, $17.00 and $10.99. Which measure of center best describes the set of prices? A mean B median C mode

Answer

C

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Teachers: Use this Mathematical Practice Pull Tab for the next 3 slides (57­59).

Math Practice

MP1 ­ Make sense of problems and persevere in solving them. Ask: How would you describe what the problem is asking? What information is given in the problem? Does the answer you get make sense for the problem's context? Which method would be most efficient for answer the problem?

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Jae bought gifts that cost $24, $26, $20 and $18. She has one more gift to buy and wants her mean cost to be $24. What should she spend for the last gift? 3 Methods : Method 1: Guess & Check

Method 1

Answer

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Jae bought gifts that cost $24, $26, $20 and $18. She has one more gift to buy and wants her mean cost to be $24. What should she spend for the last gift? Method 2: Work Backwards

Method 2

Answer

59

Method 3: Write an Equation

Jae bought gifts that cost $24, $26, $20 and $18. She has one more gift to buy and wants her mean cost to be $24. What should she spend for the last gift?

Method 3

Answer

Let x = Jae's cost for the last gift. 24 + 26 + 20 + 18 + x = 24 5 88 + x = 24 5 88 + x = 120 (multiplied both sides by 5) x = 32 (subtracted 88 from both sides)

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Your test scores are 87, 86, 89, and 88. You have one more test in the marking period. You want your average to be a 90. What score must you get on your last test?

Mean Problem

Answer

61

22 Your test grades are 72, 83, 78, 85, and 90. You have

• ne more test and want an average of an 82. What

must you earn on your next test?

Answer

62

23 Your test grades are 72, 83, 78, 85, and 90. You have

• ne

more test and want an average of an 85. Your friend figures out what you need on your next test and tells you that there is "NO way for you to wind up with an 85

• average. Is your friend correct? Why or why not?

Yes No

Answer Yes my friend is correct because I would need a 102 on the next test. 72 + 83 + 78 + 85 + 90 + x = 85 6 408 + x = 85 6 408 + x = 510 x = 102

63

Consider the data set: 50, 60, 65, 70, 80, 80, 85 The mean is: The median is: The mode is: What happens to the mean, median and mode if 60 is added to the set of data? Mean: Median: Mode:

Data Problems

Answer

64

Consider the data set: 55, 55, 57, 58, 60, 63

• The mean is:
• the median is:
• and the mode is:

What would happen if a value x was added to the set? How would the mean change:

• if x was less than the mean?
• if x equals the mean?
• if x was greater than the mean?

Data Problem Practice

Answer

65

Let's further consider the data set: 55, 55, 57, 58, 60, 63

• The mean is 58
• the median is 57.5
• and the mode is 55

What would happen if a value, "x", was added to the set? How would the median change:

• if x was less than 57?
• if x was between 57 and 58?
• if x was greater than 58?

Data Problem Practice

Answer

66

Consider the data set: 10, 15, 17, 18, 18, 20, 23

• The mean is 17.3
• the median is 18
• and the mode is 18

What would happen if the value of 20 was added to the data set? How would the mean change? How would the median change? How would the mode change?

Data Problem Practice

Answer

67

Consider the data set: 55, 55, 57, 58, 60, 63

• The mean is 58
• the median is 57.5
• and the mode is 55

What would happen if a value, "x", was added to the set? How would the mode change: if x was 55? if x was another number in the list other than 55? if x was a number not in the list?

Data Problem Practice

Answer If x was 55, the mode would stay the same at 55. If x was another number on the list

• ther than 55, there

would be another mode. If x was a number not on the list, the mode would stay the same at 55.

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24 Consider the data set: 78, 82, 85, 88, 90. Identify the data values that remain the same if "79" is added to the set. A mean B median C mode D range E minimum

Answer

69

Measures of Variation

Return to Table of Contents

70

Measures of Variation Vocabulary

Minimum ­ The smallest value in a set of data. Maximum ­ The largest value in a set of data. Range ­ The difference between the greatest data value and the least data value. Quartiles ­ are the values that divide the data in four equal parts. Lower (1st) Quartile (Q1) ­ The median of the lower half of the data Upper (3rd) Quartile (Q3) ­ The median of the upper half of the data. Interquartile Range ­ The difference of the upper quartile and the lower quartile. (Q3 ­ Q1) Outliers ­ Numbers that are significantly larger or much smaller than the rest of the data.

71

Minimum and Maximum

14, 17, 9, 2, 4, 10, 5 What is the minimum in this set of data? What is the maximum in this set of data? Answer

72

Given a maximum of 17 and a minimum of 2, what is the range?

Maximum and Minimum Practice

Answer

15

73

25 Find the range: 4, 2, 6, 5, 10, 9 A 5 B 8 C 9 D 10

Answer

B

74

26 Find the range, given a data set with a maximum value of 100 and a minimum value of 1

Answer

99

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27 Find the range for the given set of data: 13, 17, 12, 28, 35

Answer

23

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28 Find the range: 32, 21, 25, 67, 82

Answer

61

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Quartiles

There are three quartiles for every set of data. Lower Half Upper Half 10, 14, 17, 18, 21, 25, 27, 28

Q1 Q2 Q3

The lower quartile (Q1) is the median of the lower half of the data which is 15.5. The upper quartile (Q3) is the median of the upper half of the data which is 26. The second quartile (Q2) is the median of the entire data set which is 19.5. The interquartile range is Q3 ­ Q1 which is equal to 10.5.

78

To find the first and third quartile of an odd set of data, ignore the median (Q2) when analyzing the lower and upper half of the data. 2, 5, 8, 7, 2, 1, 3 First order the numbers and find the median (Q2). 1, 2, 2, 3, 5, 7, 8 First Quartile: Median: Third Quartile: Interquartile Range: What is the lower quartile, upper quartile, and interquartile range?

Analyzing Data

Answer First Quartile: 2 Median: 3 Third Quartile: 7 Interquartile Range: 7 ­ 2 = 5

79

29 The median (Q2) of the following data set is 5. 3, 4, 4, 5, 6, 8, 8 True False

Answer

80

30 What are the lower and upper quartiles of the data set 3, 4, 4, 5, 6, 8, 8? A Q1: 3 and Q3: 8 B Q1: 3.5 and Q3: 7 C Q1: 4 and Q3: 7 D Q1: 4 and Q3: 8

Answer

81

31 What is the interquartile range of the data set 3, 4, 4, 5, 6, 8, 8?

Answer

82

32 What is the median of the data set 1, 3, 3, 4, 5, 6, 6, 7, 8, 8? A 5 B 5.5 C 6 D No median

Answer

83

33 What are the lower and upper quartiles of the data set 1, 3, 3, 4, 5, 6, 6, 7, 8, 8? (Pick two answers) A Q1: 1 B Q1: 3 C Q1: 4 D Q3: 6 E Q3: 7 F Q3: 8

Answer

84

34 What is the interquartile range of the data set 1, 3, 3, 4, 5, 6, 6, 7, 8, 8?

Answer

85

Outliers ­ Numbers that are relatively much larger or much smaller than the data. Which of the following data sets have outlier(s)?

• A. 1, 13, 18, 22, 25
• B. 17, 52, 63, 74, 79, 83, 120
• C. 13, 15, 17, 21, 26, 29, 31
• D. 25, 32, 35, 39, 40, 41

Outliers Practice

Answer

A & B

86

When the outlier is not obvious, a general rule of thumb is that the

• utlier falls more than 1.5 times the interquartile range below Q1 or

above Q3. Consider the set 1, 5, 6, 9, 17. Q1: 3 Q2: 6 Q3: 13 IQR: 10 1.5 x IQR = 1.5 x 10 = 15 Q1 ­ 15 = 3 ­ 15 = ­12 Q3 + 15 = 13 + 15 = 28 In order to be an outlier, a number should be smaller than ­12 or larger than 28.

Outliers Practice

Answer Q1: 3 Q2: 6 Q3: 13 IQR: 10 1.5 x IQR = 1.5 x 10 = 15 Q1 ­ 15 = 3 ­ 15 = ­12 Q3 + 15 = 13 + 15 = 28 In order to be an outlier, a number should be smaller than ­12 or larger than 28.

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35 A B C D Which of the following data sets have outlier(s)? 13, 18, 22, 25, 100 17, 52, 63, 74, 79, 83 13, 15, 17, 21, 26, 29, 31, 75 1, 25, 32, 35, 39, 40, 41

Answer

A, B, C, D

88

36 The data set: 1, 20, 30, 40, 50, 60, 70 has an outlier which is ________ than the rest of the data. A higher B lower C neither

Answer

B Even though 1 does not follow the general rule, it is

• bvious that it does not

belong.

89

37 In the following data what number is the outlier? { 1, 2, 2, 4, 5, 5, 5, 13}

Answer

90

38 In the following data what number is the outlier? { 27, 27.6, 27.8 , 27.8, 27.9, 32}

Answer

32

91

39 In the following data what number is the outlier? { 47, 48, 51, 52, 52, 56, 79}

Answer

79

92

40 The data value that occurs most often is called the A mode B range C median D mean

Answer

A

93

41 The middle value of a set of data, when ordered from lowest to highest is the _________ A mode B range C median D mean

Answer

94

42 Find the maximum value: 15, 10, 32, 13, 2 A 2 B 15 C 13 D 32

Answer

D

95

43 Identify the outlier(s): 78, 81, 85, 92, 96, 145

Answer

96

44 If you take a set of data and subtract the minimum value from the maximum value, you will have found the ______ A

• utlier

B median C mean D range

Answer

D

97

High Temperatures for Halloween Year Temperature 2003 91 2002 92 2001 92 2000 89 1999 96 1998 88 1997 97 1996 95 Find the mean, median, range, quartiles, interquartile range and

• utliers for the data below.

Analyzing Data Practice

98

88 89 90 91 92 93 94 95 96 97

Mean Median Range Lower Quartile Upper Quartile Interquartile Range Outliers 740/8 = 92.5

92

97­88 = 9 90 95.5 5.5 None

High Temperatures for Halloween

High Temperatures for Halloween

YearTemperature 2003 91 2002 92 2001 92 2000 89 1999 96 1998 88 1997 97 1996 95

Teacher Notes & Math Practice

99

Candy Calories Butterscotch Discs Candy Corn Caramels Gum Dark Chocolate Bar Gummy Bears Jelly Beans Licorice Twists Lollipop Milk Chocolate Almond Milk Chocolate Find the mean, median, range, quartiles, interquartile range and outliers for the data. 60 160 160 10 200 130 160 140 60 210 210

Analyzing Data Practice

100

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

Mean Median Range Lower Quartile Upper Quartile Interquartile Range Outliers

1500/11 = 136.36 160 210­10 = 200 60 200 140 10

Calories from Candy

Candy Calories Butterscotch Discs Candy Corn Caramels Gum Dark Chocolate Bar Gummy Bears Jelly Beans Licorice Twists Lollipop Milk Chocolate Almond Milk Chocolate

60 160 160 10 200 130 160 140 60 210 210

101

Mean Absolute Deviation

Return to Table of Contents

102

Activity

The table below shows the number of minutes eight friends have talked

• n their cell phones in one day. In your groups, answer the following

questions.

• 1. Find the mean of the data.
• 2. What is the difference between the data value 52 and the mean?
• 3. Which value is farthest from the mean?
• 4. Overall, are the data values close to the mean or far away from

the mean? Explain.

52 48 60 55 59 54 58 62

Phone Usage (Minutes) Answer

103

The mean absolute deviation of a set of data is the average distance between each data value and the mean. Steps

• 1. Find the mean.
• 2. Find the distance between each data value and the mean.

That is, find the absolute value of the difference between each data value and the mean.

• 3. Find the average of those differences.

*HINT: Use a table to help you organize your data.

Mean Absolute Deviation

104

Let's continue with the "Phone Usage" example. Step 1 ­ We already found the mean of the data is 56. Step 2 ­ Now create a table to find the differences.

48 52 54 55 58 59 60 62

Data Value Absolute Value of the Difference |Data Value ­ Mean|

Phone Usage Practice Problem

105

Step 3 ­ Find the average of those differences. 8 + 4 + 2 + 1 + 2 + 3 + 4 + 6 = 3.75 8 The mean absolute deviation is 3.75. The average distance between each data value and the mean is 3.75 minutes. This means that the number of minutes each friend talks on the phone varies 3.75 minutes from the mean of 56 minutes.

Phone Usage Practice Problem

106

Try This! The table shows the maximum speeds of eight roller coasters at Eight Flags Super Adventure. Find the mean absolute deviation of the set of

• data. Describe what the mean absolute deviation represents.

Maximum Speeds of Roller Coasters (mph)

Mean Absolute Deviation Practice

Answer Mean is 64 mph. The mean absolute deviation is 12.5. This means that the average distance each data value is from the mean is 12.5 miles per hour.

107

45 Find the mean absolute deviation of the given set of data. Zoo Admission Prices $9.50 $9.00 $8.25 $9.25 $8.00 $8.50 A $0.50 B $8.75 C $3.00 D $9.00

Answer

108

46 Find the mean absolute deviation for the given set

• f data.

Number of Daily Visitors to a Web Site 112 145 108 160 122

Answer

109

47 Find the mean absolute deviation for the given set

• f data. Round to the nearest hundredth.

65 63 33 45 72 88

Answer

110

48 Find the mean absolute deviation for the given set

• f data. Round to the nearest hundredth.

Prices of Tablet Computers $145 $232 $335 $153 $212 $89

Answer

111

49 The median number of points scored by 9 players in a basketball game is 12. The range of the number of points scored by the same basketball players in the same game is 7. Drag and drop the correct word or phrase (on the next page) to each row of the table to indicate whether the statement is true, false, or does not contain enough information.

From PARCC EOY sample test non­calculator #2

112

true false not enough information Answer

The median number of points scored by 9 players in a basketball game is 12. The range of the number of points scored by the same basketball players in the same game is 7.

113

Glossary

Return to Table of Contents Teacher Notes

Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end

• f the presentation with the

word defined on it.

114 Back to Instruction

Analyze

To examine the detail or structure of something, in order to provide an explanation or interpretation of it. what why how when

115 Back to Instruction

Data

A collection of facts, such as values or measurements.

116 Back to Instruction

Interquartile Range

The difference between the upper and the lower quartile in a set of data.

25% 25% 25% 25%

Q1 Q2 Q3 1,3,3,4,5,6,6,7,8,8 Q1 Q2 Q3

1 2 3 4 5 6 7 8

Q1

Q2 Q3

= Q3 ­ Q1 = Q3 ­ Q1

117 Back to Instruction

25% 25% 25% 25%

Q1 Q2 Q3 1,3,3,4,5,6,6,7,8,8 Q1 Q2 Q3

1 2 3 4 5 6 7 8

Q1

Q2 Q3

Median

}

Median

}

Lower (1st) Quartile Range

The median of the lower half of a set of data.

118 Back to Instruction

Maximum

The highest or greatest amount or value.

Maximum includes the highest value.

It means ____

• r less.

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Mean

The value/amount of each item when the total is distributed across each item equally.

3 + 4 + 2 = 9

= 9 3 = 3

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Mean Absolute Deviation

The average distance between each data value and the mean

• f a set of data.

Find the mean

Subtract the mean from each data point

Find the mean of the differences

2,2,3,4,4

15 5=3

3­2=1 4­3=1 3­3=0

1+1+0+1+1 =4 5=.8

3­2=1 4­3=1

1. 2. 3.

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Measures of Center

Statistics used to describe the "center" of the distribution of data. (mean, median, mode) median

mean = 4

mode

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Median

The middle value in a set of

• rdered numbers.

1, 2, 3, 4, 5

Median

1, 2, 3, 4

Median is 2.5

1+2+3+4 = 10 10/4 = 2.5

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Minimum

The lowest or least amount or value.

You must drive at least 40 mph.

You must be at least this tall to ride. Minimum includes the smallest possible value.

It means ____

• r more.

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Mode

The number that occurs most

• ften in a set of numbers.

2, 4, 6, 3, 4

The mode is 4.

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Outlier

A value in a set of data that is much lower or much higher than the other values.

1,3,5,5,6,12

1 2 3 4 5 6 7 8 9 10 11 12

• utlier
• utlier

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25% 25% 25% 25%

Q1 Q2 Q3 1,3,3,4,5,6,6,7,8,8 Q1 Q2

Q3

1 2 3 4 5 6 7 8

Q1

Q2 Q3

Quartile

One of three values that divide a set of data into four quarters.

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Range

The difference between the lowest and the highest value in a set of data.

2, 4, 7, 12

12 ­ 2 = 10

The range is 10. 2 12

1 3 5 7 9 2 4 6 8

10

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Relatively

To evaluate something based on how it compares to something else. relatively small relatively large brother mother cousin uncle

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Upper (3rd) Quartile Range

The median of the upper half of a set of data.

25% 25% 25% 25%

Q1 Q2 Q3 1,3,3,4,5,6,6,7,8,8 Q1 Q2

Q3

1 2 3 4 5 6 7 8

Q1

Q2 Q3

Median

}

Median

}

130

Standards for Mathematical Practice MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & quantitatively. MP3: Construct viable arguments and critique the reasoning of

• thers.

MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for & make use of structure. MP8: Look for & express regularity in repeated reasoning. Additional questions are included on the slides using the "Math Practice" Pull­tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull­tab.

Math Practice