Chapter 6.4 Box and Whisker Plots
Quartile: include 𝑄 1 , 𝑄 2 , 𝑎𝑛𝑑 𝑄 3 Inter-quartile: 𝑄 3 - 𝑄 1
The box extends to the upper and lower quartiles. 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 88 88 89 90 92 Lower quartile Median 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 85 88 88 89 90 92 Median Upper quartile Lower quartile What are minimum and maximum values?
How to look at a Box Plot The least and greatest values show the range 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 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. Boys Girls 2. The boys are taller on average. 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. Drawing a Box Plot. 130 140 150 160 170 180 190 Boys Girls cm 1. The girls are taller on average. 3. The girls show less variability in height. 4. The boys show less variability in height. 5. The smallest person is a girl. 6. The tallest person is a boy.
Steps Order the data from least to greatest Find the FIVE SUMMARY Find the median ( 𝑄 2 ) Find 𝑄 1 by finding the median of the lower half of the data (the left of the median) Find 𝑄 3 by finding the median of the upper half of the data (the right of the median) Find min value and max value (lower extreme and upper extreme) Plot the FIVE SUMMARY below a number line (use a ruler to make sure your number line marks are evenly spaced) Draw the box and the whiskers
Inter-Quartile Range = 9 - 5½ = 3½ Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Order the data Lower Quartile = 5½ Q1 Median = 8 Q2 Upper Quartile = 9 Q3 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Inter-Quartile Range = 9 - 5½ = 3½
Inter-Quartile Range = 10 - 4 = 6 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 Lower Quartile = 4 Q1 Median = 8 Q2 Upper Quartile = 10 Q3 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Inter-Quartile Range = 10 - 4 = 6
Discuss the calculations below. 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Median = 8 hours and the inter-quartile range = 9 – 6 = 3 hours. Battery Life: The life of 12 batteries recorded in hours is: Mean = 93/12 = 7.75 hours and the range = 15 – 2 = 13 hours. Discuss the calculations below. 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.
Boys Girls Box Plots Box and Whisker Diagrams. 4 5 6 7 8 9 10 11 12 130 140 150 160 170 180 190 Boys Girls cm 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 Upper Quartile Highest Value Median Whisker Box 4 5 6 7 8 9 10 11 12 Box Plots
Finding the median, quartiles and inter-quartile range. worksheet Finding the median, quartiles and inter-quartile range. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Example 1: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Example 2: Find the median and quartiles for the data below. Worksheet 1
Litter Size 2 3 4 5 6 Number of Litters 1 8 11 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 8 11
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 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 quartile: 3 median of lower half Median: 4 Upper quartile: 5 median of upper half
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 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 quartile: 3 median of lower half Median: 4 Upper quartile: 5 median of upper half
c What letter is the _____? F E D Lower half Upper half B 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 A B c How do you know?
*It helps you to interpret and represent data. 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. Order the data from least to greatest. Find the median. 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 Order the values. 12 15 19 21 74 75 83 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. Order the data from least to greatest. Find the median. Find the median of the lower half – lower quartile Find the median of the upper half – upper quartile We do B. 75, 61, 88, 79, 79, 99, 63, 77 61 63 75 77 79 79 88 99 Order the values. lower quartile: = 69 63 + 75 2 upper quartile: = 83.5 79 + 88 2
Find the lower and upper quartiles for the data set. Order the data from least to greatest. Find the median. Find the median of the lower half – lower quartile Find the median of the upper half – upper quartile We do A. 25, 38, 66, 19, 91, 47, 13 Order the values. 13 19 25 38 47 66 91 lower quartile: 19 upper quartile: 66
Find the lower and upper quartiles for the data set. Order the data from least to greatest. Find the median. Find the median of the lower half – lower quartile Find the median of the upper half – upper quartile You do B. 45, 31, 59, 49, 49, 69, 33, 47 31 33 45 47 49 49 59 69 Order the values. lower quartile: = 39 33 + 45 2 upper quartile: = 54 49 + 59 2
Use the given data to make a box-and-whisker plot. I do: Additional Example 2: Making a Box-and-Whisker Plot Use the given data to make a box-and-whisker plot. 21, 25, 15, 13, 17, 19, 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 maximum: 25 lower quartile: = 16 15 + 17 2 upper quartile: = 21 21 + 21 2 median: = 19 19 + 19 2
Use the given data to make a box-and-whisker plot. 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
Use the given data to make a box-and-whisker plot. 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
Use the given data to make a box-and-whisker plot. We do Check It Out! Example 2 Use the given data to make a box-and-whisker plot. 31, 23, 33, 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 maximum: 35 lower quartile: = 25 24 + 26 2 upper quartile: = 32 31 + 33 2 median: = 30 29 + 31 2
Use the given data to make a box-and-whisker plot. 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
Use the given data to make a box-and-whisker plot. We do (cont.) Check It Out! Example 2 Continued Use the given data to make a box-and-whisker plot. Step 3. Draw the box and whiskers. 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
Step 1. Order the data from least to greatest 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
What did you learn today about box-and-whisker plots? 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-and-whisker-plots/lesson.php Learn how to create box-and-whisker. Take good notes Do QUESTIONSPROBLEMSCHALLENGE