11.2 Box-and-Whisker Plots - Mesa Public Schools
11.2Essential QuestionCOMMONCOREDrawing a Box-and-Whisker PlotWork with a partner. The numbers of first cousins of the students in a ninth-gradeclass are shown. A box-and-whisker plot is one way to represent the data visually.Numbers of First Cousins1031934524How can you use a box-and-whisker plot todescribe a data set?Learning ker Plots180133116a. Order the data on a strip of grid paper with 24 equally spaced boxes.832810514Fold the paper in half to find the median.b. Fold the paper in half again to divide the data into four groups. Because there are24 numbers in the data set, each group should have 6 numbers. Find the least value,the greatest value, the first quartile, and the third egreatestvaluec. Explain how the box-and-whisker plot shown represents the data set.leastvaluefirstquartile0MODELING WITHMATHEMATICSTo be proficient in math,you need to identifyimportant quantities ina practical 174515202530354045Numberof firstcousins50Communicate Your Answer2. How can you use a box-and-whisker plot to describe a data set?3. Interpret each box-and-whisker plot.a. body mass indices (BMI) of students in a ninth-grade classBMI171819202122232425262728b. heights of roller coasters at an amusement park80100120140160180Section 11.2200220240260Height(feet)Box-and-Whisker Plots593
11.2 LessonWhat You Will LearnUse box-and-whisker plots to represent data sets.Interpret box-and-whisker plots.Core VocabulVocabularylarryUse box-and-whisker plots to compare data sets.box-and-whisker plot, p. 594quartile, p. 594five-number summary, p. 594interquartile range, p. 595Using Box-and-Whisker Plots to Represent Data SetsCore ConceptBox-and-Whisker PlotA box-and-whisker plot shows the variability of a data set along a number lineusing the least value, the greatest value, and the quartiles of the data. Quartilesdivide the data set into four equal parts. The median (second quartile, Q2) dividesthe data set into two halves. The median of the lower half is the first quartile, Q1.The median of the upper half is the third quartile, Q3.STUDY TIPSometimes, the firstquartile is called thelower quartile and thethird quartile is called theupper quartile.median, Q2boxfirst quartile, Q1leastvaluewhiskerthird quartile, Q3whiskergreatestvalueThe five numbers that make up a box-and-whisker plot are called thefive-number summary of the data set.Making a Box-and-Whisker PlotMake a box-and-whisker plot that represents the ages of the members of abackpacking expedition in the mountains.24, 30, 30, 22, 25, 22, 18, 25, 28, 30, 25, 27SOLUTIONStep 1 Order the data. Find the median and the quartiles.leastvaluelower half18222224upper half25first quartile, 23252527median, 2528303030greatestvaluethird quartile, 29Step 2 Draw a number line that includes the least and greatest values. Graph pointsabove the number line for the five-number summary.Step 3 Draw a box using Q1 and Q3. Draw a line through the median. Drawwhiskers from the box to the least and greatest values.Age1819202122Monitoring Progress2324252627282930Help in English and Spanish at BigIdeasMath.com1. A basketball player scores 14, 16, 20, 5, 22, 30, 16, and 28 points during atournament. Make a box-and-whisker plot that represents the data.594Chapter 11Data Analysis and Displays
Interpreting Box-and-Whisker PlotsThe figure shows how data are distributed in a box-and-whisker plot.STUDY TIP14A long whisker or boxindicates that the dataare more spread out.12of the data arein each whisker.14of the dataare in the box.firstquartile, Q1of the data arein each whisker.median,thirdQ2quartile, Q3Another measure of variation for a data set is the interquartile range (IQR), whichis the difference of the third quartile, Q3, and the first quartile, Q1. It represents therange of the middle half of the data.Interpreting a Box-and-Whisker PlotT box-and-whisker plot represents the lengths (in seconds) of the songs played by aTherrock band at a econds)aa. Find and interpret the range of the data.b. Describe the distribution of the data.bcc. Find and interpret the interquartile range of the data.d. Are the data more spread out below Q1 or above Q3? Explain.dSOLUTIONSa. The least value is 160. The greatest value is 300.aSo, the range is 300 160 140 seconds. This means that the song lengthsvary by no more than 140 seconds.b. Each whisker represents 25% of the data. The box represents 50% of the data. So, 25% of the song lengths are between 160 and 220 seconds. 50% of the song lengths are between 220 and 280 seconds. 25% of the song lengths are between 280 and 300 seconds.c. IQR Q3 Q1 280 220 60So, the interquartile range is 60 seconds. This means that the middle half of thesong lengths vary by no more than 60 seconds.d. The left whisker is longer than the right whisker.So, the data below Q1 are more spread out than data above Q3.Monitoring ProgressHelp in English and Spanish at BigIdeasMath.comUse the box-and-whisker plot in Example 1.2. Find and interpret the range and interquartile range of the data.3. Describe the distribution of the data.Section 11.2Box-and-Whisker Plots595
Using Box-and-Whisker Plots to Compare Data SetsSTUDY TIPIf you can draw a linethrough the median of abox-and-whisker plot, andeach side is approximatelya mirror image of theother, then the distributionis symmetric.A box-and-whisker plot shows the shape of a distribution.Core ConceptShapes of Box-and-Whisker PlotsSkewed leftSymmetric The left whisker islonger than the rightwhisker.Skewed right The whiskers areabout the same length. The median is in themiddle of the plot. Most of the data areon the right side ofthe plot. The right whisker islonger than the leftwhisker. Most of the data areon the left side ofthe plot.Comparing Box-and-Whisker PlotsThe double box-and-whisker plot represents the test scores for your class and yourfriend’s class.Your classFriend’s class556065707580859095100Testscorea. Identify the shape of each distribution.b. Which test scores are more spread out? Explain.SOLUTIONa. For your class, the left whisker is longer than the right whisker, and most of thedata are on the right side of the plot. For your friend’s class, the whisker lengthsare equal, and the median is in the middle of the plot.So, the distribution for your class is skewed left, and the distribution for yourfriend’s class is symmetric.b. The range and interquartile range of the test scores in your friend’s class aregreater than the range and interquartile range in your class.So, the test scores in your friend’s class are more spread out.Monitoring ProgressHelp in English and Spanish at BigIdeasMath.com4. The double box-and-whisker plot represents the surfboard prices at Shop A andShop B. Identify the shape of each distribution. Which shop’s prices are morespread out? Explain.Shop AShop B0596Chapter 11100Data Analysis and Displays200300400500600700800900Surfboardprice (dollars)
11.2 ExercisesDynamic Solutions available at BigIdeasMath.comVocabulary and Core Concept Check1. WRITING Describe how to find the first quartile of a data set.2. DIFFERENT WORDS, SAME QUESTION Consider the box-and-whisker plot shown. Which is different? Find“both” answers.Find the interquartile range of the data.1Find the range of the middle half of the data.011510152015202425Find the difference of the greatest value and the least value of the data set.Find the difference of the third quartile and the first quartile.Monitoring Progress and Modeling with MathematicsIn Exercises 3– 8, use the box-and-whisker plot to findthe given measure.024681012143. least value4. greatest value5. third quartile6. first quartile7. median8. range1614. ANALYZING DATA The stem-and-leaf plot representsthe lengths (in inches) of the fishcaught on a fishing trip. Makea box-and-whisker plot thatrepresents the data.Stem012Leaf678890022344712Key: 1 0 10 inchesIn Exercises 9–12, make a box-and-whisker plot thatrepresents the data. (See Example 1.)9. Hours of television watched: 0, 3, 4, 5, 2, 4, 6, 510. Cat lengths (in inches): 16, 18, 20, 25, 17, 22, 23, 2111. Elevations (in feet): 2, 0, 5, 4, 1, 3, 2, 0, 2, 3, 612. MP3 player prices (in dollars): 124, 95, 105, 110, 95,124, 300, 190, 11415. ANALYZING DATA The box-and-whisker plotrepresents the prices (in dollars) of the entrées at arestaurant. (See Example 2.)8.75 10.5813.2514.75 18.259 10 11 12 13 14 15 16 17 18 19Price(dollars)a. Find and interpret the range of the data.b. Describe the distribution of the data.13. ANALYZING DATA The dot plot represents thenumbers of hours students spent studying for anexam. Make a box-and-whisker plot that representsthe data.c. Find and interpret the interquartile range ofthe data.d. Are the data more spread out below Q1 orabove Q3? Explain.Hours01234567Section 11.2HSCC ALG1 PE 11.02.indd 597Box-and-Whisker Plots5975/28/14 10:29 AM
16. ANALYZING DATA A baseball player scores 101 runs20. HOW DO YOU SEE IT? The box-and-whisker plotin a season. The box-and-whisker plot represents thenumbers of runs the player scores against differentopposing teams.represents a data set. Determine whether eachstatement is always true. Explain your reasoning.0Runs02468246810121410 12 14 16 18 20a. The data set contains the value 11.a. Find and interpret the range and interquartile rangeof the data.b. Describe the distribution of the data.b. The data set contains the value 6.c. The distribution is skewed right.d. The mean of the data is 5.c. Are the data more spread out between Q1 and Q2or between Q2 and Q3? Explain.21. ANALYZING DATA The double box-and-whisker plot17. ANALYZING DATA The double box-and-whisker plotrepresents the battery lives (in hours) of two brands ofcell phones.represents the monthly car sales for a year for twosales representatives. (See Example 3.)Brand ASales Rep ABrand BSales Rep B0481216202428Carssold234567Batterylife(hours)a. Identify the shape of each distribution.a. Identify the shape of each distribution.b. What is the range of the upper 75% of each brand?b. Which representative’s sales are more spread out?Explain.c. Compare the interquartile ranges of the twodata sets.c. Which representative had the single worst salesmonth during the year? Explain.d. Which brand do you think has a greater standarddeviation? Explain.e. You need a cell phone that has a battery life ofmore than 3.5 hours most of the time. Whichbrand should you buy? Explain.18. ERROR ANALYSIS Describe and correct the error indescribing the box-and-whisker plot.22. THOUGHT PROVOKING Create a data set that can1.8 2.02.22.42.62.83.0be represented by the box-and-whisker plot shown.Justify your answer.Length(cm)The distribution is skewed left. So,most of the data are on the left sideof the plot.04Maintaining Mathematical Proficiency10121416Reviewing what you learned in previous grades and lessons(Section 8.5)24. f (x) 2(x 9)(x 3)25. y 3(x 5)(x 5)26. y 4x2 16x 4827. h(x) x2 5x 14Chapter 11818median, the same interquartile range, and the samerange. Is it possible for the box-and-whisker plots ofthe data sets to be different? Justify your answer.which number is the range and which number is theinterquartile range of a data set. Explain.598623. CRITICAL THINKING Two data sets have the same19. WRITING Given the numbers 36 and 12, identifyUse zeros to graph the function.2Data Analysis and Displays
How can you use a box-and-whisker plot to describe a data set? Drawing a Box-and-Whisker Plot Work with a partner. The numbers of fi rst cousins of the students in a ninth-grade class are shown. A box-and-whisker plot is one way to represent the data visually. a. Order the da
282 Chapter 7 Data Analysis and Displays 7.2 Lesson Lesson Tutorials Key Vocabulary box-and-whisker plot, p. 282 quartiles, p. 282 Box-and-Whisker Plot A box-and-whisker plot displays a data set along a number line using medians. Quartiles divide the data set into four equal parts. The media
460 Chapter 10 Data Displays Lesson Tutorials 10.4 Lesson Key Vocabulary box-and-whisker plot, p. 460 fi ve-number summary, p. 460 Box-and-Whisker Plot A box-and-whisker plot represents a data set along a number line by using
Box 1 1865-1896 Box 14 1931-1932 Box 27 1949 Box 40 1957-1958 Box 53 1965-1966 Box 2 1892-1903 Box 14 1932-1934 Box 28 1950 Box 41 1959 Box 54 1966-1967 Box 3 1903-1907 Box 16 1934-1936 Box 29 1950-1951 Box 42 1958-1959 Box 55 1967 Box 3 1907-1911 Box 17 1936-1938 Box 30 1951-1952 Box 43 1959 Box 56 1967-1968 Box 5 1911-
A box and whisker plot is a way of showing and comparing distributions. The box represents the middle half of the data (from the 25th to the 75th percentile), . often these give a better idea of the distribution of the data than the minimum and maximum. Box plots can be drawn vertically or horizontally. Box and Whisker charts in Excel
Create a box and whisker plot using this data: 77, 99, 112, 85, 117, 68, 63. Show all 4 steps and work neatly below. The box-and-whisker plots below show a class’ test scores for two tests. What conclusions can you make? - The _ are the same for both tests. - The median for the sec
Algebra Quartiles & Box Plots 10B Box and Whisker Plots are graphs created to display data (very similar to a histogram) at a quick glance. Box and Whisker Plots can also be called Box Plots. There are 5 key pieces. Highest Value: The median of the Given the following box
Real name box-and-whisker plots. Draw a box from the lower quartile to the upper quartile. Extend a whisker from the ends of the box to the furthest observation which is no more than 1.5 times inter-quartile range from the box. Mark any observations beyond this as “outliers.”
paper (if used) should be placed inside the front cover of the answer book. Rough work should be scored through. All questions should be attempted. Candidates should note that Question 10 contains a choice. Question 1 is on Pages 10, 11 and 12. Question 2 is on Page 13. Pages 12 and 13 are fold-out pages. NATIONAL QUALIFICATIONS 2014 FRIDAY, 16 MAY 1.00 PM – 3.30 PM [X274/13/02] Page two .
