Lesson 12-3 Warm-Up

Box-and-Whisker Plots (12-3) What is “box-and-whisker plot”? How do you make a box-and-whisker plot? box-and-whisker plot: shows how data (lists of numbers) are distributed (arranged) on a number line by dividing the data into quartiles (four equal parts, like quarters are 4 equal parts of a dollar) and showing how much data is in each part (the median is the “middle” between the middle two, or second and third, quartiles) Example: Make a box-and-whisker plot of the following table. Step 1: Arrange the data in order from least to greatest and find the median [number(s) in the middle] , 308, 314, 317, 318, 318, 321, 322, 323, 326 326 327 333

Box-and-Whisker Plots (12-3) What is “box-and-whisker plot”? Step 2: Find the lower quartile (fourth) and upper quartile (fourth) by finding the medians of the lower and upper halves. , 308 314 317 318 318 321 322 323 326 326 327 333 median of lower quartile = = 315.5 median of upper quartile = = 326 Step 3: Draw a number line. Mark the highest and lowest values in the data set with points. Also mark the median and the median of the quartiles with points. Draw boxes around the middle two quartiles and “whiskers” from the boxes to the maximum (highest) and minimum (lowest) values. 314 + 317 2 326 + 326 2

Step 1 Arrange the data in order from least to greatest. Box-and-Whisker Plots LESSON 12-3 Additional Examples The data below represent in centimeters the wingspans of captured birds. Make a box-and-whisker plot. 61  35  61  22  33  29  40  62  21  49  72  75  28  21  54 Step 1 Arrange the data in order from least to greatest. Find the median. 21 21 22 28 29 33 35 40 49 54 61 61 62 72 75 Step 2  Find the lower quartile and upper quartile, which are the medians of the lower and upper halves. 21 21 22 28 29 33 35 40 49 54 61 61 62 72 75 lower quartile = 28 upper quartile = 61

1. Mark the minimum and maximum, the median, and the quartiles. Box-and-Whisker Plots LESSON 12-3 Additional Examples (continued) Step 3 Draw a number line. 1. Mark the minimum and maximum, the median, and the quartiles. 2. Draw a box from the first to the third quartiles. 3. Mark the median with a vertical segment. 4. Draw whiskers from the box to the minimum and maximum.

Box-and-Whisker Plots (12-3) What can you use a box-and-whisker plot to compare data? Example: Use box-and-whisker plots to compare the masses of orcas (killer whales) and hippopotami. Orca whale masses (in kilograms): 3,900 2,750 2,600 3,100 4,200 2,600 3,700 3,000 2,200 Hippo masses (in kilograms): 1,800 2000 3,000 2,500 3,600 2,700 1,900 3,100 2,300 Step 1: Arrange the data in order from least to greatest and find the median [number(s) in the middle] 2,200 2,600 2,600 2,750 3,000 3,100 3,700 3,900 4,200 1,800 1,900 2000 2,300 2,500 2,700 3,000 3,100 3,600 Step 2: Find the lower quartile (fourth) and upper quartile (fourth) by finding the medians of the lower and upper halves. 2,200 2,600 2,600 2,750 3,000 3,100 3,700 3,900 4,200 1,800 1,900 2000 2,300 2,500 2,700 3,000 3,100 3,600 median of lower quartile (orcas) = = 2,600 median of upper quartile (orcas) = = 3,800 2,600 + 2,600 2 3,700 + 3,900 2 median of lower quartile (hippos) = 1,950 median of upper quartile (hippos) = = 3,050 1,900 + 2,000 2 3,000 + 3,100 2

Box-and-Whisker Plots (12-3) Step 3: Draw one number line that has a big enough range to cover both sets of data. Then, draw the box and whisker plot for orcas under the number line and the box and whisker plot for hippos below that.

1. Draw a number line for both sets of data. Use the range of data Box-and-Whisker Plots LESSON 12-3 Additional Examples Use box-and-whisker plots to compare test scores from two math classes. Class A: 92, 84, 76, 68, 90, 67, 82, 71, 79, 85, 79 Class B: 78, 93, 81, 98, 69, 95, 74, 87, 81, 75, 83 1. Draw a number line for both sets of data. Use the range of data points to choose a scale. 2. Draw the first box-and-whisker plot under the umber line. 3. Draw the second box-and-whisker plot below the first one.

Box-and-Whisker Plots (12-3) What can a box-and-whisker tell you about a set of data? Example: What conclusions can you draw from the following box-and-whisker plot?   Analysis: The highest score is 90 and the lowest score is 50. At least half of the score are within 10 points of the median (75). The data is not distributed (spread out) evenly (since the quartiles aren’t evenly spaced), and a fourth of the class scored between 75 and 79 points. Example: What conclusions can you draw from the following box-and-whisker plots?.    Analysis: The percent of voters who registered (signed up) to vote stayed close to the same from year to year, since the plot is narrow (not too spread out). The percent who actually voted varied more, but it was always less than the percent who registered to vote, Therefore, you can conclude that there were usually many who were registered didn’t vote.

Describe the data in the box-and-whisker plot. Box-and-Whisker Plots LESSON 12-3 Additional Examples Describe the data in the box-and-whisker plot. The lowest score is 55 and the highest is 85. 25% of the scores are at or below 66 and one fourth of the scores are at or above 80. Half of the scores are at or between 66 and 80 and thus half or more than half of the scores are within 10 points of the median, 76.

Box-and-Whisker Plots LESSON 12-3 Additional Examples The plots below compare the percents of students who were eligible to those that participated in extracurricular activities in one school from 1992 to 2002. What conclusions can you draw? About 95% of the students were eligible to participate in extracurricular activities. Around 60% of the students did participate. A little less than two thirds of the eligible students participated in extracurricular activities.

1. Use the data to make a box-and-whisker plot. Box-and-Whisker Plots LESSON 12-3 Lesson Quiz Solve. 1. Use the data to make a box-and-whisker plot. Student heights (in.) are: 60, 66, 59, 67, 68, 63, 62, 61, 69, 64, 61. a. What is the median height? b. Between what heights do 50% of the students fall? 63 in. between 61 in. and 67 in.

Box-and-Whisker Plots LESSON 12-3 Lesson Quiz 2. The box-and-whisker plots below compare prices for the same items at Mary’s Discount Store and Ed’s Clothing. What conclusions can you draw? Prices at the discount store are more tightly grouped around the median price of $25. Half the items cost from $18 to $45. For less expensive items, there is not much difference in the prices at the two stores. For more expensive items, the discount store offers lower prices.