Chapter 6 4 Box and Whisker Plots A

Chapter 6. 4 Box and Whisker Plots

A box-and-whisker plot shows the distribution of data. The middle half of the data is represented by a “box” with a vertical line at the median. The box extends to the upper and lower quartiles. The upper quartile is the median of the upper half of the data. The lower quartile is the median of the lower half of the data. Data set: 85, 92, 78, 88, 90, 88, 89 78 85 Lower quartile 88 88 89 Median 90 92 Upper quartile What is a box-and-whisker plot? What are the upper and lower quartiles?

The lower fourth and upper fourth quarters are represented by “whiskers” that extend to the minimum (least) and maximum (greatest) values. Data set: 85, 92, 78, 88, 90, 88, 89 78 Lower quartile 85 88 88 89 Median 90 92 Upper quartile What are minimum and maximum values?

How to look at a Box Plot 1. The least and greatest values show the range 2. The width of the box shows how consistent the data is. § A wide box shows very inconsistent data § A narrow box show a very consistent data 3. The location of the median shows the distribution of the data § Towards the middle means even distribution § Towards the side shows uneven distribution

Drawing a Box Plot. Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers. Boys 130 140 150 160 170 180 cm Girls 1. The girls are taller on average. 2. The boys are taller on average. 3. The girls show less variability in height. 5. The smallest person is a girl. 4. The boys show less variability in height. 6. The tallest person is a boy. 190

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Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 5, 9, 8, 10 10, 12 Order the data Q 2 Q 1 4, 5, 6, Lower Quartile = 5½ 8, Q 3 8, Median = 8 9, 9, Upper Quartile = 9 Inter-Quartile Range = 9 - 5½ = 3½

Finding the median, quartiles and inter-quartile range. Example 2: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data Q 2 Q 1 3, 4, 6, Lower Quartile = 4 8, Median = 8 Q 3 8, 9, 10, Upper Quartile = 10 Inter-Quartile Range = 10 - 4 = 6 10, 15,

Discuss the calculations below. Battery Life: The life of 12 batteries recorded in hours is: 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Mean = 93/12 = 7. 75 hours and the range = 15 – 2 = 13 hours. 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Median = 8 hours and the inter-quartile range = 9 – 6 = 3 hours. The averages are similar but the measures of spread are significantly different since the extreme values of 2 and 15 are not included in the inter-quartile range.

Box and Whisker Diagrams. Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class. Anatomy of a Box and Whisker Diagram. Lowest Value Whisker 4 5 Median Upper Quartile Whisker Box 6 7 Highest Value 8 9 10 11 12 Boys 130 140 150 160 170 180 cm 190 Girls Box Plots

worksheet Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 5, 9, 8, 10 Example 2: Find the median and quartiles for the data below. 6, Worksheet 1 3, 9, 8, 4, 10, 8, 4, 15, 8, 10

The table below summarizes a cat breeder’s records for kitten litters born in a given year. You can divide the data into four equal part using quartiles. Litter Size 2 3 4 5 6 Number of Litters 1 6 8 11 1

You know that the median of a data set divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile. Kitten Data Lower half Upper half 233333344445555556 Upper quartile: 5 Lower quartile: 3 median of upper half median of lower half Median: 4

What letter is the _____? F E D Lower half Upper half 233333344445555556 B A How do you know? c

Importance Why do we need to know how to display and analyze data in box-and-whisker plots ? *It helps you to interpret and represent data. *It gives a visual representation of data. Tell your partner which reason is most important to you. You can use one of mine or one of your own. p/s - volunteers

Find the lower and upper quartiles for the data set. 1. 2. 3. 4. Order the data from least to greatest. Find the median of the lower half – lower quartile Find the median of the upper half – upper quartile I do A. 15, 83, 75, 12, 19, 74, 21 12 15 19 21 74 75 83 Order the values. lower quartile: 15 upper quartile: 75 How did I find the lower and upper quartiles?

Find the lower and upper quartiles for the data set. 1. Order the data from least to greatest. 2. Find the median. 3. Find the median of the lower half – lower quartile 4. Find the median of the upper half – upper quartile We do B. 75, 61, 88, 79, 99, 63, 77 61 63 75 77 79 79 88 99 lower quartile: Order the values. 63 + 75 = 69 2 79 + 88 upper quartile: = 83. 5 2

Find the lower and upper quartiles for the data set. 1. Order the data from least to greatest. 2. Find the median. 3. Find the median of the lower half – lower quartile 4. Find the median of the upper half – upper quartile We do A. 25, 38, 66, 19, 91, 47, 13 13 19 25 38 47 66 91 lower quartile: 19 upper quartile: 66 Order the values.

Find the lower and upper quartiles for the data set. 1. Order the data from least to greatest. 2. Find the median. 3. Find the median of the lower half – lower quartile 4. Find the median of the upper half – upper quartile You do B. 45, 31, 59, 49, 69, 33, 47 31 33 45 47 49 49 59 69 Order the values. 33 + 45 lower quartile: = 39 2 49 + 59 upper quartile: = 54 2

I do: Additional Example 2: Making a Box-and-Whisker Plot Use the given data to make a box-and-whisker plot. 21, 25, 13, 17, 19, 21 Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum. 13 15 17 19 19 21 21 25 minimum: 13 lower 15 + 17 quartile: 2 maximum: 25 = 16 upper 21 + 21 quartile: 2 19 median: 19 + = 19 2 = 21

I do (cont. ) Additional Example 2 Continued Use the given data to make a box-and-whisker plot. Step 2. Draw a number line and plot a point above each value from Step 1. 13 15 17 19 19 21 21 25 12 14 16 18 20 22 24 26 28

I do (cont. ) Additional Example 2 Continued Use the given data to make a box-and-whisker plot. Step 3. Draw the box and whiskers. 13 15 17 19 19 21 21 25 12 14 16 18 20 22 24 26 28

We do Check It Out! Example 2 Use the given data to make a box-and-whisker plot. 31, 23, 35, 26, 24, 31, 29 Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum. 23 24 26 29 31 31 33 35 minimum: 23 lower quartile: maximum: 35 24 + 26 = 2 25 upper quartile: 31 median: 29 + = 30 2 31 + 33 = 2 32

We do (cont. ) Check It Out! Example 2 Continued Use the given data to make a box-and-whisker plot. Step 2. Draw a number line and plot a point above each value. 23 24 26 29 31 31 33 35 22 24 26 28 30 32 34 36 38

We do (cont. ) Check It Out! Example 2 Continued Use the given data to make a box-and-whisker plot. Step 3. box and whiskers. 2. Draw the a number line and plot a point above each value. 23 24 26 29 31 31 33 35 22 24 26 28 30 32 34 36 38

Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum. Step 2. Draw a number line and plot a point above each value. Step 3. Draw the box and whiskers. Additional Guided Practice: With partners: Page 544 #1 You do: Page 544 #2

Closure What uses upper and lower quartiles, the median, the maximum, and the minimum to show a set of data? Find the lower and upper quartiles for each data set. 1. 48, 52, 68, 32, 53, 47, 51 lower = 47; upper = 53

Closure (cont. ) Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, 94 3. Make a box-and-whisker plot. 78 87 91 94 98 What did you learn today about box-and-whisker plots?

Exploration • Go to my website: thanhthuycao. weebly. com Go to Integrated Classwork April 10 and click on the website http: //www. brainingcamp. com/content/box-andwhisker-plots/lesson. php • Learn how to create box-and-whisker. Take good notes • Do QUESTIONS PROBLEMS CHALLENGE