10.3 Shapes Of Distributions - Big Ideas Math
10.3 Shapes of DistributionsHow can you describe the shape of thedistribution of a data set?1ACTIVITY: Describing the Shape of a DistributionWork with a partner. The lists at the left show the last four digitsof a set of phone numbers in a phone book.a. Create a list that represents the last digit of each phone numbershown. Make a dot plot of the data.b. In your own words, how wouldyou describe the shape of thedistribution? What single word doyou think you can use to identifythis type of distribution? Explainyour reasoning.2ACTIVITY: Describing the Shape of a DistributionWork with a partner. The lists at the right showthe first three digits of a set of phone numbersin a phone book.Data DisplaysIn this lesson, you will describe shapesof distributions.a. Create a list that represents the first digit ofeach phone number shown. Make a dot plotof the data.b. In your own words, how would you describe theshape of the distribution? What single word doyou think you can use to identify this type ofdistribution? Explain your reasoning.c. In your dot plot, draw a vertical line through themiddle of the data set. What do you notice?d. Repeat part (c) for the dot plot you constructedin Activity 1. What do you notice? Compare thedistributions from Activities 1 and 2.450Chapter 10ms green pe 1003.indd 450Data Displays1/28/15 4:15:39 PM
SkewedWhen something is skewed,3it has a slanted direction or position.ACTIVITY: Describing the Shape of a DistributionWork with a partner. The table shows theages of cellular phones owned by a groupof students.01064a. Make a dot plot of the data.23511b. In your own words, how would you describethe shape of the distribution? Compare itto the distributions in Activities 1 and 2.01231001117142202012c. Why do you think this type of distribution iscalled a skewed distribution?4MathPracticeAges of Cellular Phones(years)ACTIVITY: Finding Measures of CenterWork with a partner.a. Find the means and the medians of the data sets in Activities 1 3.Use PriorResultsb. What do you notice about the means and the medians of the data sets andthe shapes of the distributions? Explain.How is thedistribution of thedata related tothe mean andthe median?c. Which measure of center do you think best describes the data set inActivity 2? in Activity 3? Explain your reasoning.d. Using your answers to part (c), decide which measure of variation you thinkbest describes the data set in Activity 2. Which measure of variation do youthink best describes the data set in Activity 3? Explain your reasoning.5. IN YOUR OWN WORDS How can you describe the shape of thedistribution of a data set?6. Name two other ways you can describe the distribution of a data set.Use what you learned about shapes of distributions to completeExercises 3 and 4 on page 454.Section 10.3ms green pe 1003.indd 451Shapes of Distributions4511/28/15 4:15:50 PM
10.3 LessonLesson TutorialsYou can use dot plots and histograms to identify shapes of distributions.Symmetric and Skewed DistributionsStudy TiptailIf all the dots of adot plot or bars of ahistogram are about thesame height, then thedistribution is a flat, oruniform, distribution.A uniform distributionis also symmetric.tailSkewed leftEXAMPLESymmetric The “tail” of the graphextends to the left. Most data are onthe right.1 Skewed rightThe left side of thegraph is a mirrorimage of the rightside of the graph. The “tail” of the graphextends to the right. Most data are onthe left.Describing the Shapes of DistributionsDescribe the shape of each distribution.a.b.Passes –4950–5960–69FrequencyDaily Snowfall AmountsSnowfall(inches)Number of passesMost of the data are on theleft, and the tail extends tothe right.The left side of the graph isapproximately a mirror imageof the right side of the graph.So, the distributionis skewed right.So, the distributionis symmetric.Daily Spam Emails ReceivedExercises 5–81. Describe the shapeof the distribution.1452Chapter 10ms green pe 1003.indd 45223456Numberof emailsData Displays1/28/15 4:16:13 PM
8473–11030So, the distribution isskewed left.–33123434–37Most of the data are on the right,Mand the tail extends to the �25Comedy AttendanceDraw and label the axes. Then drawDa bar to represent the frequency ofeach interval.e17–218–21223714–17–211810–13T frequency table shows the ages of people watching a comedyThein a theater. Display the data in a histogram. Describe the shapeof the distribution.o–1Frequency14AgesDescribing the Shape of a Distribution2FrequencyEXAMPLEAgesComparing Shapes of DistributionsThe histogram shows the ages ofpeople watching an animated moviein the same theater as in Example 2.24FrequencyDescribe the shape ofthe distribution.Most of the data are on the left,and the tail extends to the , the distribution isskewed right.2210–13018a.Animated Movie Attendance–1314EXAMPLEAgesWhich movie has an older audience?The intervals in the histograms are the same. Most of the datafor the animated movie are on the left, while most of the datafor the comedy are on the right. This means that the peoplewatching the comedy are generally older than the peoplewatching the animated movie.So, the comedy has an older audience.Exercise 92. The frequency table shows the ages of people watching ahistorical movie in a theater.AgesFrequency10 19 20 29 30 39 40 49 50 59 60 693183640145a. Display the data in a histogram. Describe the shape ofthe distribution.b. Compare the distribution of the data to the distributionsin Examples 2 and 3. What can you conclude?Section 10.3ms green pe 1003.indd 453Shapes of Distributions4531/28/15 4:16:18 PM
10.3 ExercisesHelp with Homework1. VOCABULARY How does the shape of a symmetric distribution differ fromthe shape of a skewed distribution?2. VOCABULARY For a distribution that is skewed right, which direction doesthe tail extend? Where do most of the data lie?6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Make a dot plot of the data. In your own words, how would you describe theshape of the distribution?3.4.Miles Run per DayRaffle Tickets 121413Describe the shape of each distribution.15.6.Class SizesNumber ofstudents25 26 27 28 29 307.15 16 17 18 19 20 218.Travel Time to 59–14105–0–40AgeMinutes2 39. POLICE The frequency table shows the years of service for the police officersof Jones County and Pine County. Display the data for each county in ahistogram. Describe the shape of each distribution. Which county’spolice force has less experience? Explain.Years of Service454Height(inches)Ages of People at a ConcertFrequencyFrequencyHeights of Frequency for Jones County7151712853Frequency for Pine County359141062Chapter 10ms green pe 1003.indd 454Data Displays1/28/15 4:16:21 PM
10. REASONING What is the shape of thedistribution of the restaurant waitingtimes? Explain your reasoning.Restaurant Waiting TimesFrequency3011. LOGIC Are all distributions eitherapproximately symmetric or skewed?Explain. If not, give an 0–109012. REASONING Can you use a stem-and-leaf plotto describe the shape of a distribution? Explainyour reasoning.Minutes13. CHARITY The table shows the donation amounts received by a charityin one day.Donations 0208033050253010332050735402570a. Make a histogram of the data starting with the interval 0–14. Describe theshape of the distribution.b. A company adds 5 to each donation. Make another histogram startingwith the same first interval as in part (a). Compare the shape of thisdistribution with the distribution in part (a). Explain any differencesin the distributions.Describe the shape of the distribution of each bar graph. Matchthe letters A, B, and C with the mean, the median, and the mode of the dataset. Explain your 24A1812600Find the median, first quartile, third quartile, and interquartile range of thedata. (Section 9.4)15. 68, 74, 67, 72, 63, 70, 78, 64, 7616. 39, 48, 33, 24, 30, 44, 36, 41, 28, 5317. MULTIPLE CHOICE Sixty people participate in a trivia contest. How manyfour-person teams can be formed? (Section 7.3)A 15 B 56 C 64 Section 10.3ms green pe 1003.indd 455D 240 Shapes of Distributions4551/28/15 4:16:23 PM
REASONING Can you use a stem-and-leaf plot to describe the shape of a distribution? Explain your reasoning. 13. CHARITY The table shows the donation amounts received by a charity in one day. Donations (dollars) 20 15 40 70 20 5 25504720625540 10 50 18 20 100
Microsoft Visio Workbook Page 7 Shapes e elements that can be dragged Visio shapes are pre-drawn pictur and dropped into a diagram to visually communicate information and processes. 1-D and 2-D Shapes There are two types of shapes in Visio: one-dimensional shapes (1-D shapes) and two-dimensional shapes (2-D shapes).
Discovering Math, Geometry, Altering Shapes.or, Shape Shifting L E V E L 1 Name Date ALTERING SHAPES Shapes can be combined to make different shapes. Joining two squares makes a rectangle: Shapes can be divided to make different shapes. Dividing a rectangle along the diagonal makes two
section as shown in Figure 1. Five types of cross section shapes are covered in this document. These are: W-shapes, S-shapes, Channels or C-shapes, Structural Tees, and Angles. Properties of these shapes include cross section area, shear areas, torsion constant, moments of inertia, pro
Sort 2D shapes Make patterns with 2Dshapes Count faces on 3D shapes Count edges on 3D shapes Count vertices on 3D shapes Sort 3D shapes Make patterns with 3D shape National Curriculum Objectives Mathematics Year 2: (2G2a) Identify and describe the properties of 2-D shapes, including the
chalk pastels, pens etc. Lines, Marks, Tone, Form and Texture Begin to use simple perspective in their work using a single focal point and horizon. Shape Observe and draw shapes from observations. Draw shapes in between objects. Invent new shapes. Observe and draw shapes from observations. Draw shapes in between objects. Invent new shapes.
Developmental Levels for Composing Geometric Shapes o Children move through levels in the composition and decomposition of two-dimensional figures. o Very young children cannot compose shapes but then gain the ability to combine shapes into pictures, synthesize combinations of shapes into new shapes and eventually build new shapes.
an economy beam series consisting of 40 shapes, (2) a shallow beam series consisting of 35 shapes, (3) a deep economy beam series consisting of 8 shapes, and (4) a column series consisting of 56 shapes. Thus, there is a total of 139 proposed metric shapes compared with 295 US shapes presently listed in the AISC
Sort the 2D shapes into the correct group: Rectangle Triangle Pentagon How have the shapes been sorted? Whitney sorted her shapes by the number of sides. What shapes could belong to each group? 4 sidesNot 71. Reasoning and Problem Solving Ron sorted the shapes
