Understanding, Identifying & Analyzing Box & Whisker Plots CCSS: 6.SP.4, 8.SP.1 VA SOLs: A.10
Box and Whisker Plots Lower Extreme Lower Quartile Median Upper Quartile Upper Extreme The inter quartile range is the middle 50% of the box and whisker plot! Each section of the box and whisker plot is ¼ or 25% of the data! THINK ABOUT IT! How is a Box and Whisker Plot a lot like a One Dollar Bill? Hint:
A box and whisker plot is a unique graph that breaks data into quartiles. Each quartile, despite how wide it may appear contains the same amount of data. Think of each quartile like a quarter (25 cents). The longer the width of the plot the further apart the data is in relation to each other. The shorter the width of the plot the closer together the data is in relation to each other. Example #1 Did the value of the coin change? Did the amount of information in the quartile change? How much is it worth? What percentage of information is being reported? Example #2 Did the value of the coin change? Did the amount of information in the quartile change? How much is it worth? What percentage of information is being reported?
KEY: Identifying Box and Whisker Parts 5 key values of a B&W Blue 1 st 25% - Purple 2 nd 25% - Green Stripes 3 rd 25% - Purple Polka Dots 4 th 25 % - Orange Inter Quartile Range - Yellow 0 50 25 10 39 0 3 25 30 50 0 17 25 48 50 0 17 2530 50 0 12 25 44 50 0 5 10 15 20 25 30 35 40 45 50
Directions: Color using the key then answer the questions using the data on the next page Identifying Box and Whisker Parts Hours playing a game Assuming each set has the same number of people Data Set A KEY: 5 key values of a B&W Blue 1 st 25% - Purple 2 nd 25% - Green Stripes 3 rd 25% - Purple Polka Dots 4 th 25 % - Orange Inter Quartile Range - Yellow 0 5 10 15 20 25 30 35 40 45 50 Data Set B 0 5 10 15 20 25 30 35 40 45 50 Data Set C 0 5 10 15 20 25 30 35 40 45 50 Data Set D 0 5 10 15 20 25 30 35 40 45 50 Data Set E 0 5 10 15 20 25 30 35 40 45 50
Analyzing the Data of Box and Whisker Plots In data set A, what percent of data is greater than 10 hours? In data set B, what percent of data is less than 45 hours? In data set C, what percent of data is at least 25 hours? In data set D, what percent of data is at most 30 hours? In data set E, what percent of data is at least 45 hours? Comparing data set B and D, which has the higher percentage of students playing at least 20 hours? Comparing data set C and E, which data set has more people playing at least 25 hours? Comparing data sets A and E, which data set has more people playing at least 15 hours? In which set of data, is the Inter Quartile Range (IQR) the largest? In which set of data, is the Inter Quartile Range (IQR) the smallest? In which set of data, is the Median the largest? In which set of data, is the Median the smallest?
Analyzing the Data of Box and Whisker Plots Math Class Test scores Mrs. H s Benchmark Scores 20 students 60 70 80 90 100 Miss K s Benchmark Scores 24 students 70 75 85 90 96 Mrs. M s Benchmark Scores 16 students 70 80 83 87 98 Mrs. R s Benchmark Scores 20 students 65 75 80 85 99 How many students make up 25% of Mrs. H s class? How many students make up 25% of Miss K s class? How many students make up 25% of Mrs. M s class? How many students make up 25% of Mrs. R s class? Comparing Mrs. H s and Miss K s classes: Which class has a greater number of students scoring at least a 90 on their test? Comparing Mrs. M s and Mrs. R s classes: Which class has a greater number of students scoring at most 80 on their test? Which Class has the highest median score? Who has the most students scoring at least 75 on their test, Miss K or Mrs. R?
KEY A box and whisker plot is a unique graph that breaks data into quartiles. Each quartile, despite how wide it may appear contains the same amount of data. Think of each quartile like a quarter (25 cents). The longer the width of the plot the further apart the data is in relation to each other. The shorter the width of the plot the closer together the data is in relation to each other. Example #1 Did the value of the coin change? No, How much is it worth? it remains 25 cents Did the amount of information in the quartile change? No, What percentage of information is being reported? it remains 25 percent of the information Example #2 Did the value of the coin change? No, How much is it worth? it remains 25 cents Did the amount of information in the quartile change? No, What percentage of information is being reported? it remains 25 percent of the information
Analyzing the Data of Box and Whisker Plots KEY In data set A, what percent of data is greater than 10 hours? 50% In data set B, what percent of data is less than 45 hours? 75% In data set C, what percent of data is at least 25 hours? 50% In data set D, what percent of data is at most 30 hours? 75% In data set E, what percent of data is at least 45 hours? 25% Comparing data set B and D, which has the higher percentage of students playing at least 20 hours? Set B Comparing data set C and E, which data set has more people playing at least 25 hours? They have the same amount Comparing data sets A and E, which data set has more people playing at least 15 hours? Set E In which set of data, is the Inter Quartile Range (IQR) the largest? Set E the IQR is 30 In which set of data, is the Inter Quartile Range (IQR) the smallest? In which set of data, is the Median the largest? In which set of data, is the Median the smallest? Set A The IQR is 10 Set B The median is 36 Set A The median is 10
Analyzing the Data of Box and Whisker Plots KEY Math Class Test scores Mrs. H s Benchmark Scores 20 students 60 70 80 90 100 Miss K s Benchmark Scores 24 students 70 75 85 90 96 Mrs. M s Benchmark Scores 16 students 70 80 83 87 98 Mrs. R s Benchmark Scores 20 students 65 75 80 85 99 How many students make up 25% of Mrs. H s class? 5 How many students make up 25% of Miss K s class? 6 How many students make up 25% of Mrs. M s class? 4 How many students make up 25% of Mrs. R s class? 5 Comparing Mrs. H s and Miss K s classes: Which class has a greater number of students scoring at least a 90 on their test? Comparing Mrs. M s and Mrs. R s classes: Which class has a greater number of students scoring at most 80 on their test? Which Class has the highest median score? Who has the most students scoring at least 75 on their test, Miss K or Mrs. R? Miss K has 6 while Mrs. H has 5 Mrs. M has 4 while Mrs. R has 10 Miss K s median is 85 Miss K has 18 students scoring a 75 or more Miss R has 15