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Box and Whisker Plots Box and Whisker Plots

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I can organize and display data in a box and whisker plot. I can determine the upper and lower extremes, median, and upper and lower quartiles in a box plot. Course 3

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When we are working with a larger set of data it is much easier to separate the data into quartiles. The quartiles separate the data into four equally sized parts. There are five important values to remember if you want to divide your data into quartiles : Box and Whisker Plots Lowest Value Highest Value Median Upper Quartile Lower Quartile

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The lower extreme is the lowest value The upper extreme is the highest value The median is the middle number The lower quartile divides the lower ½ of the data into two equally sized groups The upper quartile separates the upper ½ into two equally sized groups Box and Whisker Plots Lowest Value Highest Value Median Upper Quartile Lower Quartile

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The difference between the lower quartile and the upper quartile is called the interquartile range and corresponds to the 50% of the data points that are in the middle Box and Whisker Plots Lowest Value Highest Value Median Upper Quartile Lower Quartile

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To draw a box-and-whiskers plot begin by marking the five numbers described on the previous slides with dots:

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The next step is to draw the box. The box has its sides at the LQ and the UQ and we display the median by drawing a line. Then we extend the whiskers from each quartile to the upper and lower extremes. This box-and-whiskers plot separates the data into quarters (called quartiles) with the same number of data points in each part: Quartiles

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Litter Size23456 Number of Litters 168111 The table below summarizes a veterinarians records for kitten litters born in a given year. Practice finding the values: Writing the data out would look like this: 2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6

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Course 3 Litter Size23456 Number of Litters 168111 The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 2 = 4. (1 st part) (2 nd Part) (3 rd part) (4 th Part) Kitten Data 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 Lower halfUpper half lower quartile: 3 upper quartile: 5 median of upper half Median: 4 (second quartile)

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Step 1: Find the lower extreme, lower quartile, median, upper quartile, and upper extreme: Making a Box and Whisker Plot - Practice 21, 25, 15, 13, 17, 19, 19, 21 13 15 17 19 19 21 25 Order the values. lower quartile: 15 upper quartile: 21 lower extreme: 13 median: 19 upper extreme: 25 What would the interquartile range be? 21 – 15 = 6

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Course 3 9-4 Variability 12 14 16 18 20 22 24 26 28 Step 2: draw a number line and plot a point above each value from Step 1. Lower extreme 13 13 15 17 19 19 21 25 lower quartile 15 median 19 upper quartile 21 Upper extreme 25 Making a Box and Whisker Plot

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Course 3 9-4 Variability 12 14 16 18 20 22 24 26 28 Step 3: Draw the box and whiskers: 13 15 17 19 19 21 25 Making a Box and Whisker Plot

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Comparing Final 1234T Oakland 3061221 Tampa Bay 31714 48 When data is displayed in a box and whisker plot you can visually compare the information given. It is very easy to see the five important numbers that make up a box and whisker plot. Oakland 0 3 6 9 12 15 18 Tampa Bay 0 3 6 9 12 15 18

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Compare the medians: The median for Tampa Bay is significantly greater. Oakland 0 3 6 9 12 15 18 Tampa Bay 0 3 6 9 12 15 18

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Compare the differences between the upper quartile and lower quartile for each: The difference between the upper quartile and lower quartile is the length of the box, which is slightly greater for Oakland. Oakland 0 3 6 9 12 15 18 Tampa Bay 0 3 6 9 12 15 18

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You Try: 1. Organize the given data into a box and whisker plot: The number of fish caught each day for nine days straight is 26, 17, 21, 23, 19, 28, 17, 20, and 29 2. Organize the given data into a box and whisker plot. The number of pizzas needed for each class is 6, 10, 7, 12, 9, 10, and 11 Find the interquartile range for each

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