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Box and Whisker Plots

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**I can organize and display data in a box and whisker plot.**

Course 3 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.

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Box and Whisker Plots 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: Lower Quartile Upper Quartile Median Lowest Value Highest Value

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**Box and Whisker Plots 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 Lower Quartile Upper Quartile Median Lowest Value Highest Value

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Box and Whisker Plots 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 Lower Quartile Upper Quartile Median Lowest Value Highest Value

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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 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 Size Number of Litters**

Practice finding the values: The table below summarizes a veterinarian’s records for kitten litters born in a given year. Litter Size 2 3 4 5 6 Number of Litters 1 8 11 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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Kitten Data The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4. Lower half Upper half lower quartile: 3 Median: 4 (second quartile) upper quartile: 5 median of upper half Litter Size 2 3 4 5 6 Number of Litters 1 8 11 (1st part) (2nd Part) (3rd part) (4th Part) Course 3

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**Making a Box and Whisker Plot - Practice**

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

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**Making a Box and Whisker Plot**

Course 3 9-4 Variability Making a Box and Whisker Plot Step 2: draw a number line and plot a point above each value from Step 1. Lower extreme13 lower quartile 15 median 19 upper quartile 21 Upper extreme25

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**Making a Box and Whisker Plot**

Course 3 9-4 Variability Making a Box and Whisker Plot Step 3: Draw the box and whiskers:

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Comparing Final 1 2 3 4 T Oakland 6 12 21 Tampa Bay 17 14 48 Oakland Tampa Bay 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.

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Compare the medians: Oakland Tampa Bay The median for Tampa Bay is significantly greater.

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**Compare the differences between the upper quartile and lower quartile for each:**

Oakland Tampa Bay The difference between the upper quartile and lower quartile is the length of the box, which is slightly greater for Oakland.

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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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