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Modeling Data with Bar Graphs, Histograms, and Box Plots

This activity explores different ways to model and analyze data, including bar graphs, histograms, dot plots, and box plots.

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Modeling Data with Bar Graphs, Histograms, and Box Plots

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  1. Math 8CUnit 6 – Day 7 Standard: Model and analyze data using box plots

  2. Activity • Number the following numbers in order in the 24 boxes on the slip provided. Number of First Cousins

  3. Activity • Number the following numbers in order in the 24 boxes on the slip provided. • Fold the paper in half to find the median. Make a crease. Number of First Cousins

  4. Activity • Number the following numbers in order in the 24 boxes on the slip provided. • Fold the paper in half to find the median. Make a crease. • Fold the paper in half again to divide the data into four groups. Each group should have 6 #s Number of First Cousins

  5. Activity • Now draw a number line that includes the least and the greatest value in the data set. • Graph the five numbers we just found on your number line.

  6. Must Do (4/12): 1. Make a conditional frequency table. The director had 205 dancers with mixed skills. 72 dancers were trained in both folk and classical dance. 43 trained in classical dance, but not folk. 62 dancers were not trained in either discipline. 2. If 3x– y=12, what is the value of • b. c. d. e. The value cannot be determined from the information given.

  7. 1. Make a conditional frequency table. The director had 205 dancers with mixed skills. 72 dancers were trained in both folk and classical dance. 43 trained in classical dance, but not folk. 62 dancers were not trained in either discipline.

  8. Historgams, Bar Graphs, Dot andBox and Whisker plots • We can model data in many different graphical ways: • Scatter plots • Tables • Coordinate graphs • Bar Graphs • Histograms • Dot plots • Box (and whisker) plots • … and many more • Today we will explore bar graphs, histograms and dot plots.

  9. Bar Graphs vs. Histograms

  10. Modeling Data • Bar graphs and histograms look very similar, but what is different about them? • Bar Graph:

  11. Modeling Data • Bar graphs and histograms look very similar, but what is different about them? • Histogram:

  12. Bar Graphs vs. Histograms • Categorical Data • Separate bars • Uses categories for bins • Order doesn’t matter for categories • Vertical scale is frequency • Numerical Data • Bars right next to each other • Uses number ranges for bins • Number ranges must be in order • Vertical scale is frequency

  13. Example • A small survey of colors of student’s backpacks showed the following. • Which is more appropriate for this data? Histogram or Bar Graph? • Bar graph, since these data are categorical.

  14. Example • A bunch of fish were caught in a lake. Don't worry, we'll throw them back in after we're done with this example. The lengths of the fish, in inches, were6.2, 6.2, 6.55, 7, 7.4, 8.5, 8.6, 9, 9.1, 9.2, 9.25, 9.3, 10.4, 10.5, 10.6. • Histogram or bar graph? • Histogram, since these data are numerical.

  15. Must Do (4/13): 2. The incomplete table summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right- handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student is selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.) a. 0.410 b. 0.357 c. 0.333 d. 0.250 X+y=18 5x+9y=122 (10,8) 50/140 = 0.357 Bar graph or histogram? Draw it! Flight delays (in minutes) for a given day: 0,0,6,10,10,10,15,15,15,15,15,15,15,15,25,25,25,25,30,30,30,30,30,35,35,35,35, 40,40,40,45,45,50

  16. Bar graph or histogram? Draw it! Flight delays: 0,0,6,10,10,10,15,15,15,15,15,15,15,15,25,25,25,25,30,30,30,30,30,35,35,35,35, 40,40,40,45,45,50

  17. Dot Plots • Transportation officials collect data on flight delays (the number of minutes past the scheduled departure time that a flight takes off). • Here is a dot plot of the delay times for sixty BigAir flights during December, 2012

  18. Could we call this data distribution skewed or symmetric? • Skewed. The data are mostly clustered to the left, or we could say that it has a tail to the right. It’s not shaped like a normal bell curve.

  19. Box and Whisker Plots • Box plots cut a set of data into quarters by using medians, and displays it along a number line. • Quartiles mark the division of these quarters. • The median divides the data set into two halves. • The median of the lower half is the first quartile. The median of the upper half is the third quartile. • The five numbers that make up the box-and-whisker plot are called the five number summary of the data set.

  20. Box and Whisker Plots • With a box around the 1st, 2nd, and 3rd quartiles, and whiskers connecting the least value to and the greatest value with , we get a Box & Whisker Plot • Identify the five number summary:

  21. Example • Make a box plot for the ages of the member of the U.S. women’s wheelchair basketball team. 24, 30, 30, 22, 25, 22, 18, 25, 28, 30, 25, 27 Step 1: Order the data from least to greatest. Find the median and quartiles. Step 2: Draw a number line that includes the least and greatest values. Graph points above the number line for the five-number summary. Step 3: Draw a box using the quartiles. Draw a line through the median. Draw whiskers from the box to the least & greatest values.

  22. Example • Make a box plot for the ages of the member of the U.S. women’s wheelchair basketball team. 24, 30, 30, 22, 25, 22, 18, 25, 28, 30, 25, 27

  23. Create a box-and-whisker plot for the following data: 95, 60, 88, 77, 80, 84, 82, 83, 100, 84, 81, 85, 73, 50, 84 Label the median, Q1, Q3, least value, and greatest value.

  24. Compare and Contrast • These box plots show the test score distributions of two eighth-grade standardized tests. One test was taken in the fall and the other in the spring. • Compare the results • Which box plot represents the test scores from each test? How can you tell?

  25. Create a box-and-whisker plot for the following data: 95, 60, 88, 77, 80, 84, 82, 83, 100, 84, 81, 85, 73, 50, 84 Label the median, Q1, Q3, least value, and greatest value.

  26. 2. The incomplete table summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right- handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student is selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.) a. 0.410 b. 0.357 c. 0.333 d. 0.250 X+y=18 5x+9y=122 (10,8)

  27. In Class Practice U6D7 – ICP

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