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Exploring Measures of Central Tendency with Box and Whisker Plots

Learn how to analyze data using measures of central tendency, quartiles, and box and whisker plots. Practice creating frequency histograms and box and whisker plots with provided examples.

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Exploring Measures of Central Tendency with Box and Whisker Plots

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  1. BEFORE THE BELL RINGS • Please copy your homework into your assignment book

  2. Thursday, December 8, 2016 • Warm-up • Box and Whisker Plot • Practice • Homework: Frequency and Histograms HW

  3. Measures of central tendency describe how data tends toward one value. You may also need to know how data is spread out across several values. Quartiles divide a data set into four equal parts. Each quartile contains one-fourth of the values in the set. The interquartile range (IQR) is the difference between the upper and lower quartiles. The IQR represents the middle half of the data.

  4. A box-and-whisker plot can be used to show how the values in a data set are distributed. The minimum is the least value that is not an outlier. The maximum is the greatest value that is not an outlier. You need five values to make a box-and-whisker plot: the minimum, first quartile, median, third quartile, and maximum.

  5. Example 5: Sports Application The number of runs scored by a softball team at 19 games is given. Use the data to make a box-and-whisker plot. 3, 8, 10, 12, 4, 9, 13, 20, 12, 15, 10, 5, 11, 5, 10, 6, 7, 6, 11 Step 1 Order the data from least to greatest. 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 15, 20 Step 2 Identify the five needed values and determine whether there are any outliers.

  6. Minimum Maximum Q2 Q3 Q1 6 10 12 20 3 Example 5 Continued 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11,12, 12, 13, 15, 20

  7. First quartile Third quartile Minimum Maximum Median ● ● ● ● ● 0 8 16 24 Example 5 Continued Half of the scores are between 6 and 12 runs per game. One-fourth of the scores are between 3 and 6. The greatest score earned by this team is 20.

  8. NOTES For the following test scores: 65,67,72,72,75,82,83, 85, 86,88,91,91,93,94, 96, 97,98,99,99 • Find the A) mean, B)median, C) mode D) range 2. Use the data to create a stem and leaf plot 3. Use the data to create a frequency table and frequency histogram 4. Use the data to create a box and whisker plot

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