How do you draw a box and whisker plot for the following data set: 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19?

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To draw a box and whisker plot (also known as a whisker plot) for the given data set, you’ll want to follow the steps outlined below:

  1. Collect Data: Start with the data points: 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19.
  2. Sort the Data: Rank the data in ascending order: 19, 20, 20, 21, 21, 25, 25, 26, 28, 28, 29, 29, 30, 32, 35, 35, 35, 36.
  3. Determine the Five-Number Summary:
    • Minimum: The smallest value is 19.
    • First Quartile (Q1): The median of the first half of the data is 25.
    • Median (Q2): The median of the entire data set is 28.
    • Third Quartile (Q3): The median of the second half of the data is 35.
    • Maximum: The largest value is 36.
  4. Plot the Box:
    • Draw a number line that accommodates the range of your data.
    • Plot the first quartile (Q1), median (Q2), and third quartile (Q3) as vertical lines.
    • Draw a box from Q1 to Q3, with the median line inside the box.
  5. Add Whiskers:
    • Extend lines (whiskers) from the edges of the box (Q1 and Q3) to the minimum and maximum values, respectively.
    • Whiskers should not exceed 1.5 times the interquartile range (IQR). If they do, you can plot outliers as individual points.
  6. Identify Outliers:
    • To find outliers, calculate the IQR: Q3 – Q1 = 35 – 25 = 10.
    • Determine lower and upper bounds for outliers: Lower Bound = Q1 – 1.5 * IQR = 25 – 15 = 10; Upper Bound = Q3 + 1.5 * IQR = 35 + 15 = 50.
    • All data points in range (19, 36) are within bounds, so there are no outliers.

In conclusion, you will have a box and whisker plot that clearly illustrates the distribution of your data. It provides a visual representation of the median, quartiles, and any potential outliers, making it an excellent tool for data analysis and comparison.

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