6Th Grade Math At-Home Learning Packet

At-HomeLearning Instructions for 5.11-5.22

6th grade Math At-Home Learning Packet

Notes & Assignments for 5.11-5.22

Lesson: 10.4 Interquartile Range and Box Plots ○ p. 561-566 ○ Work through the lesson: complete Learn- Examples- Check- Apply Assignment: Practice 10.4 F riday 5.15 ● P.567-568 ● You will need to submit this assignment to your teacher

Lesson 10.6 Outliers ○ p. 575-580 ○ Work through the lesson: complete Learn- Examples- Check- Apply Assignment: Practice 10.6 D ue Friday 5.22 ● P.581-582 ● You will need to submit this assignment to your teacher

THIS MATERIAL

IS Copyright © McGraw-Hill Education PROVIDED median. Themedianisalsoknownasthe In thegivendataset, IQRis6.5 data istothemedian. the closermiddlehalf ofthe lower theIQRisforadataset, middle 50%,ofthedata. represents themiddlehalf, or The interquartilerange quartile fromthethirdquartile. third quartilesofthedataset.To findtheIQR,subtractfirst The Quartiles can findthismeasure, youfirstneedtounderstandandfindquartiles. Another measureofvariationisthe 0, 0, 1,2,3,4,5,6,7, 7, 7, 8 the datasetshown. between thegreatestandleastdatavaluesinaset.Consider One measureofvariationisthe vary spread, ofadataset.Theydescribehowthevaluesset Measures variation of Learn Can... I quartile is themedianofdatavalueslessthanmedian.The set in a box plot, and summarize the data. the summarize and boxplot, a in set data numerical a display value, single a with set data a of variability 0, 0, 1,2,3,4,5,6,7, 7, 7, 8 5 25% 25%

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562 of the data values? of the data values? Explain your reasoning. Which value, the Which value, the interquartile range, or the first quartile, third quartile tells you more about the spread Do the data values Do the data values need to be in Why? numerical order? Your Notes Your the spread of the data, specifically the spread of the middle half of the data. Sample answer: The interquartile range tells you more about yes; You need to find find to need You yes; the middle number. MATERIAL

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IS Copyright © McGraw-Hill Education PROVIDED contains the samenumberofvalues, 25%ofthedata. mean therearemoredata valuesinthatsection.Eachsection are morespreadoutinthat section.Alongerbox orwhisker doesnot middle 50%ofthedata. Alongerbox orwhisker indicatesthedata length, eachcontain25% ofthedata.Thetwoboxes representthe representations ofquartiles.Eventhoughtheparts maydifferin Box plotsseparatedataintofour sections.Thesesectionsarevisual with averticalline, andseparatesthebox intotwoboxes. are veryfarapartfromtherestofdataset.Themedianismarked from eachquartiletotheextreme datavalues,unlesstheextremes A box isdrawnaroundthetwoquartilevalues.Thewhiskers extend are referredtoasthe and leastvaluesinthedataset.Theextremes, quartiles,andmedian extreme values.Theextreme values,orextremes, arethegreatest distribution ofadatasetbyplottingthemedian,quartiles,and A Learn Describe thevariationofdatausinginterquartilerange. B Part using therange. Describe thevariationofdata A Part range todescribehowthedatavary. table. Usetherangeandinterquartile cities inPennsylvania aregiveninthe The averagewindspeedsforseveral Check

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Go Online Go your work work your EDUCATIONAL The average gas mileage, in miles per gallon, for various sedans is in miles per gallon, for The average gas mileage, the distribution of the data. What plot. Describe shown in the box gas mileage for those sedans? does it tell you about the average The box plot shows the annual snowfall totals, in inches, for a certain for a certain totals, in inches, the annual snowfall plot shows The box years. a period of 20 city over it tell you about of the data. What does Describe the distribution city? the snowfall in this to about 250 ranges from about 110 inches The annual snowfall 140 inches to half of the data range from about inches. The middle are shorter than the whiskers, about 195 inches. Because the boxes middle half of the data. Having less there is less variation among the consistency among the middle variation means there is a greater 50% of the data than in either whisker. Check Vendor: LDL Vendor: Program: MSM INDIVIDUAL Statistical Statistical Measures and Displays FOR responses. ’ PROVIDED Module 10 • IS

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564 195 inches. So, in half in half 195 inches. So, of the years, the city received between 140 inches and 195 inches of snow. Sample answer: The middle 50% of the data is clustered between about 140 inches and What does the interquartile range describe in the context of the problem? See students What does the length What does and of the box you about tell whiskers of the data the spread plot? in the box MATERIAL

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IS Copyright © McGraw-Hill Education PROVIDED 50% ofthedata thanineitherwhisker. more variationmeansthere isalesserconsistencyamongthemiddle there ismorevariationamong themiddlehalfofdata.Having 34 milesperhour. Becausetheboxes arelongerthan thewhiskers, hour. Themiddlehalfofthedatarange from22milesperhourto The recordedspeedsrangefrom19milesperhour to40milesper B Part Step 3 country The tableshowstherecordedspeedsofcarstravelingona Find themedian,extremes, andthefirstthirdquartiles.Graph Step 2 27, 30, 34,35,and40milesperhour. In orderfromleasttogreatest,thespeedsare19, 20, 22,23,25, Step 1 Part A distribution ofthedata. Construct abox plottorepresentthedata.Thendescribe the valuesaboveanumberline. 52 25 20 15 Example 3 Example 52 25 20 15 FOR 25

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Program: MSM Program: Vendor: LDL Construct and Interpret BoxPlots Interpret and Construct Q 1 : 22 22 Median: 25 Car Speeds (mph) Speeds Car 34 PURPOSES 03 045 40 35 30 40 Q 3 : 34 greatest value. Addatitle. from thethirdquartileto to theleastvalue. Drawaline Draw alinefromthefirstquartile Draw alinethroughthemedian. quartile andthethirdquartile. Draw abox aroundthefirst ONLY Component: Component: Grade: 6-8 Grade: 20 AND MAY 19 Extreme: 40 NOT Lesson Upper Lesson 10-4 • 10-4 Lesson 23 BE DOWNLOADED, 25

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FURTHER 9 7 3 OR km 1 km to 7 5 4 km. 6 2 10 REPRODUCED, 9 11 1 4 10 12 14 16 DOWNLOADED, 5 15 BE km and half of them occurred at km and half of them occurred at Best used to… Best used to… Best used to… 6 9 5 NOT Depth of Earthquakes (km) Recent km; half of the earthquakes occurred km; half of the earthquakes km. Because the left whisker and left km. Because the left whisker 6 MAY 6 AND Depths of Earthquakes (km) Depths of Earthquakes ONLY 2468 km. The middle half of the data range from km. The middle half of the data range 15 It’s time to update your Foldable, located in the time to update your Foldable, It’s

dot plot box plot less variation means there is a greater consistency among less variation means there is a greater that have a depth of less than the earthquakes Sample answer: The earthquake depths range from Sample answer: The earthquake to km. The median is at a depth greater than a depth less than there and right box, are shorter than the right whisker box half of the data. Having is less variation among the lower PURPOSES You can complete an Extra You Example online. histogram

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566 MATERIAL THIS NAME ______DATE ______PERIOD ______

Practice 10.4 Interquartile Range and Box Plots Practice

1. Cameron surveyed her friends about the 2. The table shows the number of hours different number of apps they use. The responses animals spend sleeping per day. Use the range and were 15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 interquartile range to describe how the data vary. apps. Use the range and interquartile range (Example 1) to describe how the data vary. (Example 1) Time Animals Spend Sleeping (h) 12 20 16 11 4 2

3. The box plot shows the ages of vice presidents when they took office. Describe the distribution of the data. What does it tell you about the ages of vice presidents? (Example 2)

4. The ages of children taking a hip-hop dance class are 10, 9, 9, 7, 12, 14, 14, 9, and 16 years old. Construct a box plot of the data. Then describe the distribution of the data. (Example 3)

5. Open Response The cost of tents on sale at a sporting goods store are $66, $72, $78, $69, $64, $70, $67, $72, and $66. Use the range and interquartile range to describe how the data vary.

Interquartile Range and Box Plots Practice 567 Apply

6. The table shows the number of points scored by Points Scored per Game the seventh and eighth grade girls basketball Seventh Grade Team Eighth Grade Team teams in each of their games this season. Construct a box plot to represent the data for 39 36 40 27 34 36 47 40 each team. Then use the box plots to compare the 35 29 36 29 39 38 45 43 data. 31 38 30 34 42 41 45 42

7. Justify Conclusions Determine if the following 8. Create Provide a set of real-world data and then statement is true or false. If false, justify your construct a box plot of the data. reasoning.

You can determine the mean of a data set from a box plot.

9. Make an Argument A student said that, in a box 10. Reason Inductively What can you conclude plot, if the box to the right of the median is about a data set shown in a box plot where the longer than the box to the left of the median, whiskers and boxes are all the same length? there are more data values represented by the longer box. Is the student’s reasoning correct? Construct an argument to defend your solution.

Interquartile Range and Box Plots Practice 568 THIS MATERIAL

IS Copyright © McGraw-Hill Education Below is a box-and-whisker of the data above. Theoutlier 780of must Belowisabox-and-whisker thedataof above. PROVIDED be taken out of the data set when you create the box-and-whisker. betakenthedatawhen outofset you create thebox-and-whisker. asterisk (*). The box plotrepresentsthedata set.Outliersareindicatedwithan contain anyvaluesthatarelessthan37.5, theonlyoutlier is780. outliers. So, thevalue780isanoutlier. Becausethedatasetdoesnot Any datavaluesthataregreaterthan737.5 orlessthan 37.5 are Q Limit Upper Determine theupperandlowerlimitsforoutliers. interquartile rangeeitheraboveQ An outlierisdefinedasavaluethatliesmorethan1.5timesthe considered outliers? How doyouknowifeitheroftheextreme values,225or780, are values. Considerthedatasetshown. values. Itcanbemuchgreaterinvalueorlessthantheother An Learn Can... I when describing a data set that does or does not contain an outlier.an contain not does or does that set data a describing when use to appropriate most is center of measure which determine and outlierbecause ismuchit bigger theotherthanof values. most 3

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Think About It! Think About Talk About It! About Talk

576 person is an extreme person is an extreme value in the data set and is significantly less than the other data values. What does it mean that 23 is an outlier? Sample answer: The age of the youngest identify any outliers? median, quartiles, interquartile range What measures of What measures do you need variation to find in order to Your Notes Your MATERIAL

575-582_MSM_SE_C1M10_L6_899714.indd THIS THIS MATERIAL

IS Copyright © McGraw-Hill Education PROVIDED Explore Because 42 Q outliers. set. Itisalsoanoutlier, because42islessthanthelowerlimitfor temperature ismuchlowerthantheothertemperaturesindata Suppose thatthehightemperatureonSaturdayis42°F. This results arerecordedinthetableshown. temperatures foroneweekandthe Suppose youtrackthedailyhigh center and/orvariation. If adatasetcontainsanoutlier, theoutliermayaffectmeasuresof Learn outliers affectthemeanandmedian. 1

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EDUCATIONAL 42 68 Program: MSM Vendor: LDL Vendor: To see how an outlier affects the measures of center and variation, variation, and of center measures the outlier affects how an see To the outlier. without with and both measures the calculate with the outlier. the measures Calculate Mean To the nearest tenth, the MAD is the To Median The median is ______• • To the nearest tenth, the MAD is the nearest tenth, To Median The median is The median was not affected by the inclusion of the outlier. Without The median was not affected by the inclusion of the outlier. With the and IQR all increased in value. the mean, MAD, the outlier, because the mean is not the best representation of center, outlier, most of the values are higher than 67.7. any Use either the mean or median when the data does not contain While outliers. Use only the median when the data contains an outlier. the median might change a little when an outlier is included or removed, it does not change as much as the mean. Use the corresponding measure of variation to describe the spread of the data. Calculate the measures without the outlier. Calculate the measures without Mean Mean (MAD) Absolute Deviation Mean (MAD) Absolute Deviation INDIVIDUAL Statistical Statistical Measures and Displays FOR PROVIDED Module 10 • IS

Talk About It! About Talk

578 temperature was added, the mean but decreased to 70, the median was unchanged. Sample answer: The Sample answer: mean and median without Saturday’s temperature was 72, when Saturday’s qualify as an outlier, qualify as an outlier, the but is cooler than rest. How does this the affect the mean? median? Suppose Saturday’s Saturday’s Suppose had been temperature which does not 59°F, MATERIAL

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IS Copyright © McGraw-Hill Education PROVIDED The Mean the nearesttenth,ifnecessary. Mean the nearesttenth,ifnecessary. median withtheoutlier. Round to Median Median The meanlifespanisabout The meanlifespanisabout Step 3 The medianlifespanis ___ Step 2 The medianlifespanis ____ Step 1 the center. describes best that measure the choose Then 200. outlier, the without and with median and mean the Calculate lifespans ofselectedanimals. The tableshowstheaverage The So, the 35 35

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≈ Animal ONLY 62.1 Grade: 6-8 Grade: Component: Component: Average Lifespan Average AND MAY NOT Lesson Lifespan BE (years) 200 DOWNLOADED, 50 20 30 30 35 70 PDF Pass PDF REPRODUCED, Lesson 10-6 • 10-6 Lesson years orless. lifespans thatare50 of theanimalshave Sample answer:Most around 39or62years. years, ratherthan around 32.5or35 the tablearecentered of theanimalslistedin sense thatthelifespan Explain whyitmakes responses. See students’ your reasoning. median more? Explain the meanor Will theoutlieraffect ThinkAbout It! Talk About It! OR Outliers FURTHER 09/11/18

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364.3 NOT ≈ Lesson 340.6 MAY ≈ AND ONLY Component: Grade: 6-8 See students’ observations. See students’ PURPOSES You can complete an Extra You Example online. mean with outlier: mean with outlier: 350 median with outlier: mean without outlier: outlier: 350 median without by the The mean was affected the most Sample answer: not change when the The median temperature did outlier. be the best measure of outlier was removed, so it would center to represent the data set.

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580 MATERIAL

575-582_MSM_SE_C1M10_L6_899714.indd THIS NAME ______DATE ______PERIOD ______

Practice 10-6: Outliers Practice

1. Last week, Joakim spent 40, 25, 60, 30, 35, and 2. Last month, a basketball team scored 83, 84, 85, 40 minutes practicing the piano. Identify any 87, 89, 88, 67, 79, and 81 points in their games. outliers in the data. (Example 1) Identify any outliers in the data. (Example 1)

3. Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 4. Last week a certain pet store had 52, 72, 96, 21, boxes of cookies after different football games. 58, 40, and 75 paying customers. Identify any Identify any outliers in the data. (Example 1) outliers in the data. (Example 1)

5. The prices of trees that Sahana bought are $46, 6. The prices of backpacks are $37, $43, $41, $36, $39, $40, $45, $44, $68, and $51. Calculate the $44, and $70. Calculate the mean and median mean and median with and without the outlier. with and without the outlier. Round to the Round to the nearest tenth, if necessary. nearest tenth, if necessary. Choose the Choose the measure that best describes the measure that best describes the center. center. (Example 2) (Example 2)

7. The table shows the number of points scored Points Scored by a Football Team by a football team. Calculate the mean and 14 20 3 9 median with and without the outlier. Round to the nearest tenth, if necessary. Choose the 18 35 21 24 measure that best describes the center. 7 12 31 68 Explain. (Example 2)

Outliers Practice 581 8. Multiple Choice The table shows the Points Scored in a Trivia Game number of points scored by the players in a trivia game. Which measure of center 12 9 5 11 best represents the data? 6 0 14 7

A mean B median C mode D range

Apply

9. Create Generate a set of real-world data that 10. Justify Conclusions The ages, in years, of contains two outliers. participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, and 11. Identify any outliers in the

data set. Justify your response.

11. Construct an Argument Explain how an outlier 12. Justify Conclusions Does an outlier affect the may or may not affect the mean and median. range of a data set? Explain.

Outliers Practice 582