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Statistics: Describing Quantitative Data

Statistics: Describing Quantitative Data. Box and Whisker Plots. Do Now. Complete Problem #2 in the stem and leaf packet regarding American vs. National baseball averages. Questions?!?!. Any questions on stem and leaf plots in general? Ask now!!! Please!. Box and Whisker Plots.

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Statistics: Describing Quantitative Data

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  1. Statistics: Describing Quantitative Data Box and Whisker Plots

  2. Do Now • Complete Problem #2 in the stem and leaf packet regarding American vs. National baseball averages.

  3. Questions?!?! • Any questions on stem and leaf plots in general? Ask now!!! Please!

  4. Box and Whisker Plots • Displays 5 pieces of information: • 1. Minimum • 2. Q1 • 3. Median • 4. Q3 • 5. Maximum

  5. Q1/Q3 • Q1/Q3: The medians of the lower/upper half of the data. • Upper Quartile/Lower Quartile • 25th/75th percentile

  6. IQR • Interquartile Range: • IQR= Q3 – Q1 • Another way to describe spread • IF you describe center as the median, use IQR as the measure for spread.

  7. Creating Box/Whisker Plots • Create a vertical axis • Draw in a horizontal line to indicate Q1, median and Q3. Create a box around them. • Determine the “fences” • Q3+1.5IQR • Q1-1.5IQR • NOTE: Anything outside these fences is considered an outlier! So it will be drawn in with a special (i.e. *) symbol. • Complete the display with whiskers to the min/max of the data INSIDE the fences, then add on *’s as needed for the outliers.

  8. Example One: • In 1961 Roger Maris made baseball headlines by hitting 61 home runs, breaking a famous record held by Babe Ruth. Here are Maris’s home run totals for his 10 seasons. Create a box and whisker plot to display the data. Would you consider his record-setting year to be an outlier? 8 13 14 16 23 26 28 33 39 61

  9. Interpreting Box Plots

  10. Overall • Symmetric Data: • The mean/median should be close together • The boxplot should be relatively symmetrical • Skewed Left: • The median will be smaller than the mean • The median will be closer to Q3 than Q1 • The left whisker will be longer than the right • Skewed Right: • The median will be larger than the mean • The median will be closer to Q1 than Q3 • The right whisker will be longer than the left.

  11. Example Three:

  12. Practice Problems • Try some on your own/in small groups

  13. Exit Ticket • Is the following data skewed or symmetric. If skewed, tell me which way. EXPLAIN yourself.

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