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Box and Whisker Plots

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## Box and Whisker Plots

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**Box and Whisker Plots**SWBAT create, read, and identify the values of a box and whisker plot.**A box plot summarizes data using the median, upper and**lowerquartiles, and the extreme (least and greatest) values. It allows you to see important characteristics of the data at a glance.**Example Problem: The gas mileages in miles per gallon**(mpg) of 4-cylinder manual transmission cars are in a table on the next slide**24 25 28 28 29 29 29 30 30 31 31 32 32 32 33 34 37 38 38 39**42 44 44 44 To make a box plot, organize the data by arranging the data in order from least to greatest.**24 25 28 28 29 29 29 30 30 31 31 32 32 32 33 34 37 38 38 39**42 44 44 44Find the median of the data. It is 32This divides the data in half. The lower half : 24 25 28 28 29 29 29 30 30 31 31 32 and the upper half: 32 32 33 34 37 38 38 39 42 44 44 44**Find the median of the top half of the data. 32 32 33 34 37**38 38 39 42 44 44 44This is called the high median, upper quartile or quartile 3. It is 38.**Take the lower half of the data and find the median of it.24**25 28 28 29 29 29 30 30 31 31 32This data, 29, is called the low median, lower quartile or quartile 1.**Next, find the lower and upper extremes. This simply means**the lowest data, 24, and the highest data, 44.Let’s organize all 5 pieces of data together so we can see them.**Lower extreme = 24Lower quartile(Q1) =29Median (Q2)**= 32Upper quartile(Q3) =38Upper extreme(Q4)=44The data is now divided into quartiles(4ths) so each quartile represents one-fourth of the data.**Next, make a number line that will best display the 5 pieces**of data (24 29 32 38 44)**Place a dot above the number line to show the lower extreme**and one for the upper extreme.**Put a vertical slash above the number line for the median**and one for the lower and upper quartiles.**Enclose the vertical slashes into a box. Draw a line from**the right center of the box to the upper extreme and one from the lower end of the box to the lower extreme, forming the whiskers.**You must label the number line to tell what the data**represents.Miles per gallon (mpg)**All graphs must have a title that clearly represents what**your graph is showing. Miles per Gallon of 4-cylinder Cars Miles per gallon (mpg)**Interpreting the Box Plot:**Study your Box and Whisker Plot to determine what it is telling you. Make a statement about what it is saying, then support the statement with facts from your graph.**You should include the following in your interpretation:**• Range or spread of the data and what it means to your graph • Quartiles—compare them. What are they telling you about the data? • Median- this is an important part of the graph, and should be an important part of the interpretation. • Percentages should be used to interpret the data, where relevant.**We will now interpret the data we have on mpg of 4-cylinder**cars. We will do this step-by-step, then put all the interpretation together as our final summary.**Miles per Gallon of 4-cylinder Cars**Miles per gallon (mpg)**Make a statement about what it is saying, then support the**statement with facts from your graph: The Box and Whisker Plot clearly shows that are a lot of different gas mileages on various 4-cylinder vehicles**Miles per Gallon of 4-cylinder Cars**Miles per gallon (mpg)**Range or spread of the data and what it means to your graph**The mileage ranged from 24 miles per gallon(mpg) to a high of 44 mpg. This is a 20 miles per gallon spread, which in car mileage is quite a bit of difference.**Quartiles—compare them. What are they telling you about**the data? The first quartile reads as 32 mpg which means that 75% of the vehicles in this study got 32 mpg or more. The 3rd quartile tells us that 25% of these cars got 38 mpg or higher which is really good mileage.**Median- this is an important part of the graph, and should**be an important part of the interpretation. The median cuts the data in half. The median is 32 mpg. Therefore half the cars in the study received 32 mpg or higher.