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Measures of Position - Quartiles and Box and Whisker Plots

Learn how to calculate quartiles and create box and whisker plots to analyze data sets. Compare measures of central tendency.

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Measures of Position - Quartiles and Box and Whisker Plots

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  1. Warm-Up m = 9 Solve for x: x = 0

  2. Measures of Position –QuartilesBox and Whisker Plots The three quartiles Q1, Q2, and Q3 approximately divide an ordered data set into four equal parts. About ¼ of the data falls on or below the first quartile Q1. About ½ of the data falls below the second quartile Q2., and about ¾ of the data falls below the third quartile Q3. The second quartile and the median of the data set are the same number

  3. Measures of Position - Quartiles • To find the quartiles: • Order the data • Find Q2 (the Median): • If there is an odd number of data points, find the center data point, Q2 • If there are an even number of data points, find the center gap, and average the numbers on either side of the gap.

  4. Measures of Position - Quartiles • To find the quartiles: • Find Q1: • If there is an odd number of data points below Q2, find the center data point, and call it Q1 • If there are an even number of data points below Q2, find the center gap, and average the numbers on either side of the gap, and label it Q1. • Find Q3: • If there is an odd number of data points above Q2, find the center data point, and call it Q3 • If there are an even number of data points above Q2, find the center gap, and average the numbers on either side of the gap, and label it Q3. • The interquartile Range (IQR) equals Q3 – Q1.

  5. Measures of Position - Quartiles • To make a box and whisker plot: • Make a number line and label Q1, Q2, and Q3 • Make a rectangular box using Q1 and Q3 as ends • Mark a vertical line at Q2 • Mark the minimum and maximum data points • Draw a horizontal line from the minimum point to Q1. • Draw a horizontal line from Q3 to the maximum point

  6. Measures of Position - Quartiles • Make a box-and-whisker plot of the following data, and identify any outliers: • 5, 6, 4, 6, 3, 7, 5, 3, 4, 5, 6, 5, 3, 2, 4, 4, 4 • First, order the data: • 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7 • Find the center data point:

  7. Measures of Position - Quartiles • Make a box-and-whisker plot of the following data, and identify any outliers: • 5, 6, 4, 6, 3, 7, 5, 3, 4, 5, 6, 5, 3, 2, 4, 4, 4 • First, order the data: • 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7 • Find the center data point: 4 • Find Q1:

  8. Measures of Position - Quartiles • Make a box-and-whisker plot of the following data, and identify any outliers: • 5, 6, 4, 6, 3, 7, 5, 3, 4, 5, 6, 5, 3, 2, 4, 4, 4 • First, order the data: • 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7 • Find the center data point: 4 • Find Q1: have to average 3 and 4, giving 3.5 • Find Q3:

  9. Measures of Position - Quartiles • Make a box-and-whisker plot of the following data, and identify any outliers: • 5, 6, 4, 6, 3, 7, 5, 3, 4, 5, 6, 5, 3, 2, 4, 4, 4 • First, order the data: • 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7 • Find the center data point: 4 • Find Q1: have to average 3 and 4, giving 3.5 • Find Q3: have to average 5 and 6, giving 5.5

  10. Measures of Position - Quartiles • Make a box-and-whisker plot of the following data, and identify any outliers: • 5, 6, 4, 6, 3, 7, 5, 3, 4, 5, 6, 5, 3, 2, 4, 4, 4 • First, order the data: • 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7 • Find the center data point: 4 • Find Q1: have to average 3 and 4, giving 3.5 • Find Q3: have to average 5 and 6, giving 5.5 • Find the IQR:

  11. Measures of Position - Quartiles • Make a box-and-whisker plot of the following data, and identify any outliers: • 5, 6, 4, 6, 3, 7, 5, 3, 4, 5, 6, 5, 3, 2, 4, 4, 4 • First, order the data: • 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7 • Find the center data point: 4 • Find Q1: have to average 3 and 4, giving 3.5 • Find Q3: have to average 5 and 6, giving 5.5 • Find the IQR: Q3 – Q1 = 5.5 – 3.5 = 2.0

  12. Compare: • Compare the SAD, mean deviation, and box and whisker plot of the following data sets, and tell which measure of central tendency is best for each one • NOTE: When comparing box plots, you should use the same scale and stack them • Set A: 45, 56, 40, 50, 98, 60 • Set B: 23, 45, 60, 34, 12

  13. Homework • Pg 365 # 9 – 12 all and 15 • Pg 371, # 1 – 7 all

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