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 Due Friday 5.22 ● P.581-582 ● You will need to submit this assignment to your teacher Lesson 10-4 Interquartile Range and Box Plots I Can... understand how a measure of variation describes the What Vocabulary variability of a data set with a single value, display a numerical data Will You Learn? set in a box plot, and summarize the data. box plot first quartile interquartile range Learn Measures of Variation measures of variation Measures of variation are values that describe the variability, or quartiles spread, of a data set. They describe how the values of a data set range vary with a single number. second quartile third quartile One measure of variation is the range, which is the difference between the greatest and least data values in a data set. Consider the data set shown. The data values range from 0 to 8. 0, 0, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8 The range is 8–0, or 8. Another measure of variation is the interquartile range. Before you can find this measure, you first need to understand and find quartiles. Quartiles divide the data into four equal parts. The first quartile, Q1, is the median of the data values less than the median. The third quartile, Q3, is the median of the data values greater than the Talk About It! median. The median is also known as the second quartile, Q2. How does knowing Median (Q2) = 3.5 that the data is divided The median divides the data into four equal parts Q1 = 1.5 Q3 = 6.5 into two halves. The quartiles help you remember divide the data into fourths. the vocabulary term 25% 25% 25% 25% Each fourth represents 25% quartile? of the data. 0, 0, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8 See students’ responses. Lower Half Upper Half Talk About It! The interquartile range (IQR) is the distance between the first and third quartiles of the data set. To find the IQR, subtract the first If the median describes the center Copyright © McGraw-Hill Education Copyright © McGraw-Hill quartile from the third quartile. IQR = 6.5 - 1.5, or 5 of a data set, what The interquartile range does the interquartile represents the middle half, or Q1 = 1.5 Q3 = 6.5 range describe? middle 50%, of the data. The Sample answer: The lower the IQR is for a data set, 25% 25% 25% 25% the closer the middle half of the interquartile range 0, 0, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8 data is to the median. describes how spread 50% out the middle 50% of the values are around In the given data set, the IQR is 6.5 - 1.5, or 5. the median. Lesson 10-4 • Interquartile Range and Box Plots 561 THIS MATERIAL IS PROVIDED FOR INDIVIDUAL EDUCATIONAL PURPOSES ONLY AND MAY NOT BE DOWNLOADED, REPRODUCED, OR FURTHER DISTRIBUTED. Your Notes Example 1 Find the Range and Interquartile Range The table shows the approximate Animal Speed (mph) maximum speeds, in miles per hour, of different animals. Housecat 30 Think About It! Cheetah 70 Use the range and interquartile range Do the data values to describe how the data vary. Elephant 25 need to be in numerical order? Why? Lion 50 Part A Describe the variation of the Mouse 8 yes; You need to find data using the range. Spider 1 the middle number. The greatest speed in the data set is 70 miles per hour. The least speed in the data set is 1 mile per hour. The range is 70 - 1, or 69 miles per hour. The speeds of animals vary by 69 miles per hour. Talk About It! Which value, the interquartile range, the Part B Describe the variation of the data using the interquartile first quartile, or the range. third quartile tells you more about the spread Step 1 Find the median. of the data values? Write the speeds in order from least to greatest. Explain your reasoning. Sample answer: The 1 8 25 30 50 70 interquartile range tells you more about least greatest Find the mean of the two middle numbers, the spread of the The median is 27.5 . data, specifically the 25 and 30. spread of the middle Education Copyright © McGraw-Hill Step 2 Find the first and third quartiles. half of the data. The first quartile is 8 . Find the median of the lower half of the data. The third quartile is 50 . Find the median of the upper half of the data. Step 3 Find the interquartile range. Interquartile range = Q 3 - Q 1 = 50 - 8 Q 3 = 50; Q 1 = 8 = 42 Subtract. So, the spread of the middle 50% of the data is 42 . This means that the middle half of the data values vary by 42 miles per hour. 562 Module 10 • Statistical Measures and Displays THIS MATERIAL IS PROVIDED FOR INDIVIDUAL EDUCATIONAL PURPOSES ONLY AND MAY NOT BE DOWNLOADED, REPRODUCED, OR FURTHER DISTRIBUTED. 561-568_MSM_SE_C1M10_L4_899714.indd 09/11/18 03:39PM 561-568_MSM_SE_C1M10_L4_899714.indd Program: MSM Component: Lesson PDF Pass Vendor: LDL Grade: 6-8 Check The average wind speeds for several Wind Speed cities in Pennsylvania are given in the City Speed (mph) table. Use the range and interquartile range to describe how the data vary. Allentown 8.9 Erie 11.0 Part A Harrisburg 7.5 Describe the variation of the data Middletown 7.7 using the range. Philadelphia 9.5 Show The data vary by a range of your work Pittsburgh 9.0 here 3.5 miles per hour. Williamsport 7.6 Part B Math History Minute Describe the variation of the data using the interquartile range. Florence Nightingale Show The middle half of the data values vary by 1.9 (1820–1910) used your work here miles per hour. statistics to help improve the survival rates of hospital patients. She Go Online You can complete an Extra Example online. discovered that by improving sanitation, survival rates improved. Learn Construct Box Plots She designed charts to A box plot, or box-and-whisker plot, uses a number line to show the display the data, as distribution of a data set by plotting the median, quartiles, and statistics had rarely been presented with extreme values. The extreme values, or extremes, are the greatest charts before. She is and least values in the data set. The extremes, quartiles, and median known for inventing the are referred to as the five-number summary. coxcomb graph, which A box is drawn around the two quartile values. The whiskers extend is a variation of the from each quartile to the extreme data values, unless the extremes circle graph. are very far apart from the rest of the data set. The median is marked with a vertical line, and separates the box into two boxes. lower upper extreme Q1 median Q2 extreme Copyright © McGraw-Hill Education Copyright © McGraw-Hill Box plots separate data into four sections. These sections are visual representations of quartiles. Even though the parts may differ in length, each contain 25% of the data. The two boxes represent the middle 50% of the data. A longer box or whisker indicates the data are more spread out in that section. A longer box or whisker does not mean there are more data values in that section. Each section contains the same number of values, 25% of the data. Lesson 10-4 • Interquartile Range and Box Plots 563 THIS MATERIAL IS PROVIDED FOR INDIVIDUAL EDUCATIONAL PURPOSES ONLY AND MAY NOT BE DOWNLOADED, REPRODUCED, OR FURTHER DISTRIBUTED. 30/11/18 05:14PM 561-568_MSM_SE_C1M10_L4_899714.indd 30/11/18 05:14PM Program: MSM Component: Lesson PDF Pass Vendor: LDL Grade: 6-8 Example 2 Think About It! Interpret Box Plots What does the length The box plot shows the annual snowfall totals, in inches, for a certain of the box and city over a period of 20 years. whiskers tell you about the spread of the data Annual Snowfall (in.) in the box plot? See students’ responses. 100 120 140 160 180 200 220 240 260 Describe the distribution of the data. What does it tell you about the snowfall in this city? The annual snowfall ranges from about 110 inches to about 250 Talk About It! inches. The middle half of the data range from about 140 inches to What does the about 195 inches. Because the boxes are shorter than the whiskers, interquartile range there is less variation among the middle half of the data. Having less describe in the context variation means there is a greater consistency among the middle of the problem? 50% of the data than in either whisker. Sample answer: The middle 50% of the data Check is clustered between The average gas mileage, in miles per gallon, for various sedans is about 140 inches and shown in the box plot. Describe the distribution of the data. What 195 inches. So, in half does it tell you about the average gas mileage for those sedans? of the years, the city received between 140 Average Gas Mileage (mpg) inches and 195 inches of snow.