6th Grade

Statistical Variability

2017­02­16

www.njctl.org Table of Contents

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What is Statistics? Measures of Center Mean Median Mode Central Tendency Application Problems Measures of Variation

Minimum/Maximum Teacher Notes Range Quartiles Outliers Mean Absolute Deviation Glossary What is Statistics? Teacher Notes

Return to Table of Contents Data

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

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 Conclusions

MP7 ­ Look for and make use Lets put statistics to work! of structure. Two 6th grade math classes Ask: took the same end of unit test. • What do you notice about every data point within the Here are their results. same class? Class 1: • How do the two class' data Math Practice 89, 88, 92, 78, 85, 89, 95, 71, 100, 88, points relate to each other? 97, 82, 77, 98, 86, 82, 95, 88 • What patterns do you notice between the data points? Class 2: 100, 53, 92, 91, 97, 93, 92

What conclusions can you draw by looking at the numbers? Statistics

When we just look at a list of numbers, it can take a lot of time to make sense of what we are dealing with.

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

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

Class 1 average: 88Click

Class 2: 100, 53, 92, 91, 97, 93, 92

Class 2 average: 88 Click

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? Graphing Statistics Look at the graphs below to see the results in another way.

MP3 ­ Construct viable arguments and critique the reasoning of others. For #3 Ask: • What mathematical evidence would support your answer of fair or not fair? • What were you considering when giving your answer? • What is the same and different Math Practice The red line on the graph marks the class average. about your answer vs another students? Discuss the following questions with your group. • Is there a "right" answer to this 1. How does the number of students in each class affect the scores? question or can both answers be 2. How do the student scores compare to the average in each class? correct? How can you tell? 3. Is the average a fair way to compare the two classes scores? Why or why not? Statistics

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 Example

Lets use these statistical tools to compare the 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 Range

• 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 Outliers • 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 Mean Deviation

• 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 outlier was eliminated, the mean would be 94 and would more accurately reflect the majority of the students' scores. Statistics Example

Discuss the following question with your group. MP7 ­ Look for and make use After looking more closely at the data, of structure. what conclusions can we draw? Ask: • What do you notice about every data point within the same class?

Math Practice • How do the two class' data points relate to each other? • What patterns do you notice between the data points? 1 Statistics is the study of data.

True False

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

True

False

True Answer 3 The purpose of statistics is to: (Select all that apply)

A Collect numerical information

B Organize numerical data

C Analyze numerical information A, B, C, D Answer D Interpret numerical data Statistical Questions

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 How many cupcakes each type were made by were made by the bakery the bakery last week? last week? How many cupcakes did How many cupcakes did I each person in my class eat last week? eat last week? 4 Which statistical question best fits the data graphed below?

A How many glasses of milk does each member of our class drink a day? A

B How many letters are in the last name of each class Answer 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? 5 Which statistical question best fits the data graphed below?

C Answer 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? 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? C

D What is the difference in height between the oak Answer tree and the pine tree?

From PARCC EOY sample test non­calculator #12 Statistical Toolbox

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. Measures of Center

Return to Table of Contents 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 MP2 ­ Reason abstractly and quantitatively. • How many tiles does your group have in total? Ask: • • How can you equally share all the tiles? How many would each What are the different cards Teacher Notes

& Math Practice representing? member receive? (Ignore the color) • • What are the different colors Each member has a different number of tiles according to color. representing? Write out a list of how many tiles each person has from least to • How can you tell which information is greatest. Look at the two middle numbers. What number is in relevant to decide what the values are? between these two numbers? 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. Vocabulary

Measures of Center:

• Mean ­ The sum of the data values divided by the number of items; average • Median ­ The middle data value when the values are written in numerical order • Mode ­ The data value that occurs the most often 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. Answer Mean Practice

Find the mean

10, 8, 9, 8, 5 Answer 7 Find the mean

20, 25, 25, 20, 25

23 Answer 8 Find the mean

14, 17, 9, 2, 4,10, 5, 3 Answer Median Practice

Given the following set of data, what is the median?

10, 7, 9, 3, 5 7 What do we do when finding the median of an even set of numbers? MP6 ­ Attend to precision.

Before students solve have them think about... • Do we need an exact value? • How can we use what we know Answer about the median to make a

& Math Practice guess? • What are the cons of having a rounded value? • What place value should we round to if necessary? Median Practice

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 Answer 9 Find the median: 5, 9, 2, 6, 10, 4

A 5

B 5.5 C 6 D 7.5 B Answer 10 Find the median: 15, 19, 12, 6, 100, 40, 50

A 15

B 12 C 19 D 6 C Answer 11 Find the median: 1, 2, 3, 4, 5, 6

A 3 & 4 B 3 C 4 D D 3.5 Answer 12 What number can be added to the data set below so that the median is 134?

54, 156, 134, 79, 139, 163

Any number less than or equal to 133 Answer 13 What number can be added to the data set below so that the median is 16.5?

17, 9, 4, 16, 29, Answer Mean, Median, and Data

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 The mean is 6 and the median is coins each student found. 7.

10, 7, 3, 8, 2 The mean tells us that if the data were evenly distributed, each Find the mean and median of the data. What does the mean and median tell us about the data? student would have 6 coins.

Teacher Notes The median tells us that half the class has more than 7 coins and the other half has less than 7. Mode Practice

Find the mode

10, 8, 9, 8, 5 MP8 ­ Look for and express regularity in repeated reasoning Ask: Find the mode Answer ­What do we now about the mode that & Math Practice we can apply to this new situation? 1, 2, 3, 4, 5 ­How is this new situation similar to finding the mode in the first place? Different? What can be added to the set of data above, so that there are two modes? Three modes? 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 A & D

E 10 Answer 15 What value(s) must be eliminated so the data set has 1 mode: 2, 2, 3, 3, 5, 6 ?

2 or 3 Answer 16 Find the mode(s): 3, 4, 4, 5, 5, 6, 7, 8, 9

A 4 B 5 C 9 D No mode A & B Answer 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 Central Tendency Application Problems

Return to Table of Contents Teachers: Use this Mathematical Practice Pull Tab to MP4 ­ Model with mathematics compliment slides 48­51. Have students explore other real­ life situations of statistics. Have students come up with examples to share with each other. You can also have students come up with their Teacher Notes

& Math Practice own examples of a data set for other students to choose the appropriate measure of center to find. Which Measure of Center to Use?

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?

Find the mean, median and mode and compare them. Which Measure of Center to Use?

13 ft, 2 ft, 19 ft, 18 ft and 16 ft

Mean: 13.6 ftClick Median: 16 ftClick Mode: no modeClick

Which measure of center best describes the data?

Click The median is closest to most of the values, so it best describes the data.

The mean is less than 3 out of the 5 values, and there was no mode. Using Measures of Center to Describe Data

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?

Brand A $1.25 Brand D $0.99 Brand B $0.95 Brand E $1.99 Brand C $1.09 Brand F $0.99 Measures of Center Data In order to see how the measures of 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. Mean: $1.21 The Mean is greater than most of the data.

Median: $1.04 Half of the data is greater than the median, and half of the data is less than the median. Mode: $0.99 The mode reflects the lower 4 values very well, but is much lower than the top two values. 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 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 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 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 Answer C mode Teachers: Use this Mathematical Practice Pull Tab for the next 3 slides (57­59). 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 Math Practice sense for the problem's context? • Which method would be most efficient for answer the problem? Guess and Check

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 Answer Work Backwards

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? In order to have a mean of $24 on 5 gifts, the sum of all 5 gifts must be $24 x 5 = $120. Method 2: Work Backwards The sum of the first four gifts is $88. So the last gift should

Answer cost $120 ­ $88 = $32. 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? Let x = Jae's cost for the last gift. Method 3: Write an Equation Answer

x = 32 (subtracted 88 from both sides) Mean Problem

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? Answer 22 Your test grades are 72, 83, 78, 85, and 90. You have one more test and want an average of an 82. What must you earn on your next test? Answer 23 Your test grades are 72, 83, 78, 85, and 90. You have one 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 Data Problems

Consider the data set: 50, 60, 65, 70, 80, 80, 85

The mean is:

The median is: Answer

The mode is:

What happens to the mean, median and mode if 60 is added to the Note: Adding 60 to the data set lowers the mean and the median. set of data?

Mean:

Median:

Mode: Data Problem Practice 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? If x was less than the mean, the mean would decrease. How would the mean change:

• if x was less than the mean? Answer If x equaled the mean, the • if x equals the mean? mean would not change. • if x was greater than the mean? If x was greater than the mean, the mean would increase. Data Problem Practice If x was less than 57, the Let's further consider the data set: 55, 55, 57, 58, 60, 63 median would decrease to 57. • The mean is 58 • the median is 57.5 If x was between 57 and 58, the • and the mode is 55 median increase or decrease to that number added between 57 What would happen if a value, "x", was added to the set?

Answer and 58. How would the median change: • if x was less than 57? If x was greater than 58, the • if x was between 57 and 58? median would increase to • if x was greater than 58? 58. Data Problem Practice

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? Answer Data Problem Practice Consider the data set: 55, 55, 57, 58, 60, 63 • The mean is 58 • the median is 57.5 • and the mode is 55 If x was 55, the mode would stay the same at 55. What would happen if a value, "x", was added to the set? If x was another number on How would the mode change: the list other than 55, there • if x was 55? would be another mode. • if x was another number in the list other than 55? Answer • if x was a number not in the list? If x was a number not on the list, the mode would stay the same at 55. 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 C, D, E D range

E minimum Answer Measures of Variation

Return to Table of Contents 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. Minimum and Maximum

14, 17, 9, 2, 4, 10, 5

What is the minimum in this set of data?

Answer

What is the maximum in this set of data? Maximum and Minimum Practice

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

Answer 25 Find the range: 4, 2, 6, 5, 10, 9

A 5 B 8 C 9 D 10 B Answer 26 Find the range, given a data set with a maximum value of 100 and a minimum value of 1.

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

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

61 Answer 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. Analyzing Data 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: 2 Median: 3 What is the lower quartile, upper quartile, and interquartile range? Third Quartile: 7 Answer Interquartile Range: 7 ­ 2 = 5

First Quartile: Median: Third Quartile: Interquartile Range: 29 The median (Q2) of the following data set is 5.

3, 4, 4, 5, 6, 8, 8

True

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

4 Answer 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 5.5 D No median Answer 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 D Q3: 6 B Q1: 3 E Q3: 7 C Q1: 4 F Q3: 8 B & E Answer 34 What is the interquartile range of the data set 1, 3, 3, 4, 5, 6, 6, 7, 8, 8?

4 Answer Outliers Practice

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 A & B

B. 17, 52, 63, 74, 79, 83, 120 Answer

C. 13, 15, 17, 21, 26, 29, 31

D. 25, 32, 35, 39, 40, 41 Outliers Practice When the outlier is not obvious, a general rule of thumb is that the outlier 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 Answer

In order to be an outlier, a number should be smaller than ­12 or larger than 28. 35 Which of the following data sets have outlier(s)?

A 13, 18, 22, 25, 100

B 17, 52, 63, 74, 79, 83

C 13, 15, 17, 21, 26, 29, 31, 75 Answer D 1, 25, 32, 35, 39, 40, 41 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 B C neither Even though 1 does not follow the general rule, it is Answer obvious that it does not belong. 37 In the following data what number is the outlier? { 1, 2, 2, 4, 5, 5, 5, 13}

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

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

79 Answer 40 The data value that occurs most often is called the ____.

A mode B range C median A D mean Answer 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 C Answer 42 Find the maximum value: 15, 10, 32, 13, 2

A 2 B 15 C 13 D 32 D Answer 43 Identify the outlier(s): 78, 81, 85, 92, 96, 145

145 Answer 44 If you take a set of data and subtract the minimum value from the maximum value, you will have found the ____.

A outlier B median C mean D range D Answer Analyzing Data Practice Find the mean, median, range, quartiles, interquartile range and outliers for the data below.

High Temperatures for Halloween

Year Temperature 2003 91 2002 92 2001 92 2000 89 1999 96 1998 88 1997 97 1996 95 High Temperatures for Halloween Use the data from the chart to create a line plot. One way to organize your data is to create a line plot. Write the numbers below the line and place an "x" above High Temperatures for Halloween the number each time it appears in the data set. MP5 ­ Use appropriate tools strategically. Ask: Teacher Notes & Math Practice What information is given in the problem? What mathematical tools can you use to organize the given information to help find the data points?

88 89 90 91 92 93 94 95 96 97 Line Plots Use the line plot to find each measure of variation.

Mean: 740/8 = 92.5 Click Median: 92 Click

Range: 97 ­ 88 = 9 Lower Quartile: 90 Click Click

Upper Quartile: 95.5 Interquartile Range: 5.5 Click Click

Outliers: NoneClick

High Temperatures for Halloween

x x x x x x x x

88 89 90 91 92 93 94 95 96 97 Analyzing Data Practice

Find the mean, median, range, quartiles, interquartile range and outliers for the data.

Candy Calories Butterscotch Discs 60 Candy Corn 160 Caramels 160 Gum 10 Dark Chocolate Bar 200 Gummy Bears 130 Jelly Beans 160 Licorice Twists 140 Lollipop 60 Milk Chocolate Almond 210 Milk Chocolate 210 Calories from Candy Use the data to complete the line plot

Candy Calories Butterscotch Discs 60 Candy Corn 160 Caramels 160 Gum 10 Dark Chocolate Bar 200 Gummy Bears 130 Jelly Beans 160 Licorice Twists 140 Lollipop 60 Milk Chocolate Almond 210 Milk Chocolate 210

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 Calories from Candy Use the line plot to find each measure of variation.

Mean: 1500/11 = 136.36 Click Upper Quartile: 200Click

Median: 160ClickClick Interquartile Range: 140Click

Range: 210­10 = 200Click Outliers: 10Click

Lower Quartile: 60Click

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

Return to Table of Contents Activity

The table below shows the number of minutes eight friends have talked on 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 Answer the mean? Explain.

Phone Usage (Minutes)

52 48 60 55 59 54 58 62 Mean Absolute Deviation

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. Phone Usage Practice Problem 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.

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

Click

Click

Click

Click

Click

Click

Click

Click Phone Usage Practice Problem

Step 3 ­ Find the average of those differences.

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. Mean Absolute Deviation Practice 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) Answer 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 Answer D $9.00 46 Find the mean absolute deviation for the given set of data.

Number of Daily Visitors to a Web Site

112 145 108 160 122 Answer 47 Find the mean absolute deviation for the given set of data. Round to the nearest hundredth.

65 63 33 45 72 88 Answer 48 Find the mean absolute deviation for the given set of data. Round to the nearest hundredth.

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

true

false Answer

not enough information Vocabulary Words are bolded in the presentation. The text box the word is in is then Glossary linked to the page at the end of the presentation with the Teacher Notes word defined on it.

Return to Table of Contents Analyze To examine the detail or structure of something, in order to provide an explanation or interpretation of it.

what why how when

Back to Instruction Data A collection of facts, such as values or measurements.

Back to Instruction Interquartile Range

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

Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3

25% 25% 25% 25% 1,3,3,4,5,6,6,7,8,8 1 2 3 4 5 6 7 8 = Q3 ­ Q1 = Q3 ­ Q1

Back to Instruction Lower (1st) Quartile Range

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

Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3

25% 25% 25% 25% 1,3,3,4,5,6,6,7,8,8 } } 1 2 3 4 5 6 7 8 Median Median

Back to Instruction Maximum

The highest or greatest amount or value.

Maximum includes the highest value.

It means ____ or less.

Back to Instruction Mean

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

3 + 4 + 2 = 9

= 9 3 = ÷ 3

Back to Instruction Mean Absolute Deviation The average distance between each data value and the mean of a set of data.

1. Find the mean 2. Find the Subtract 3­2=1 3. mean of the the mean 3­2=1 differences 3­3=0 2,2,3,4,4 from each data point 4­3=1 4­3=1 1+1+0+1+1 15 5=÷ 3 =4 5=÷ .8

Back to Instruction Measures of Center

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

mode mean = 4 median

Back to Instruction Median

The middle value in a set of ordered numbers.

1+2+3+4=10 1, 2, 3, 4 1, 2, 3, 4, 5 10/4 = 2.5

Median Median is 2.5

Back to Instruction Minimum

The lowest or least amount or value.

Minimum includes the smallest possible value. You must drive at least You must be at least It means ____ 40 mph. this tall to ride. or more.

Back to Instruction Mode The number that occurs most often in a set of numbers.

2, 4, 6, 3, 4

The mode is 4.

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

outlier 1,3,5,5,6,12

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

Back to Instruction Quartile One of three values that divide a set of data into four quarters.

Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3

25% 25% 25% 25% 1,3,3,4,5,6,6,7,8,8 1 2 3 4 5 6 7 8

Back to Instruction Range The difference between the lowest and the highest value in a set of data.

1 2 3 4 5 6 7 8 9 10 12 ­ 2 = 10 2, 4, 7, 12 2 12 The range is 10.

Back to Instruction Relatively To evaluate something based on how it compares to something else.

brother mother relatively relatively cousin uncle small large

Back to Instruction Upper (3rd) Quartile Range

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

Q1 Q2 Q1 Q2 Q3 Q1 Q2 Q3 Q3

25% 25% 25% 25% 1,3,3,4,5,6,6,7,8,8 } } 1 2 3 4 5 6 7 8 Median Median

Back to Instruction Standards for Mathematical Practices Throughout this unit, the Standards for Mathematical Practice are used. MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & quantitatively. MP3: Construct viable arguments and critique the reasoning of others. 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.