Box and Whisker Plot Worksheet Answers

Understanding Box and Whisker Plots

A box and whisker plot is a graphical representation of a dataset that displays the distribution of values in a clear and concise manner. It is a powerful tool for summarizing and visualizing data, especially when working with large datasets. In this worksheet, we will explore the components of a box and whisker plot, learn how to read and interpret them, and practice creating our own plots.

Components of a Box and Whisker Plot

A box and whisker plot consists of several key components:

• Median (Q2): The middle value of the dataset, which splits the data into two equal parts.
• Quartiles (Q1 and Q3): The values that divide the data into four equal parts, with Q1 being the median of the lower half and Q3 being the median of the upper half.
• Interquartile Range (IQR): The difference between Q3 and Q1, which represents the spread of the middle 50% of the data.
• Whiskers: The lines that extend from the box to the minimum and maximum values of the dataset, which represent the range of the data.
• Outliers: Data points that fall more than 1.5 times the IQR away from the edges of the box.

Reading and Interpreting Box and Whisker Plots

To read and interpret a box and whisker plot, follow these steps:

1. Identify the median: Look for the line inside the box, which represents the median value.
2. Determine the quartiles: Identify the edges of the box, which represent Q1 and Q3.
3. Calculate the IQR: Subtract Q1 from Q3 to find the IQR.
4. Examine the whiskers: Look at the length and direction of the whiskers to understand the range of the data.
5. Check for outliers: Look for data points that fall outside the whiskers, which may indicate unusual or erroneous values.

Creating a Box and Whisker Plot

To create a box and whisker plot, follow these steps:

1. Organize the data: Arrange the data in order from smallest to largest.
2. Find the median: Calculate the median value of the dataset.
3. Determine the quartiles: Calculate Q1 and Q3 using the median.
4. Calculate the IQR: Subtract Q1 from Q3.
5. Draw the box: Draw a box with the edges at Q1 and Q3, and a line inside the box at the median.
6. Add the whiskers: Draw lines from the edges of the box to the minimum and maximum values of the dataset.

Example Problems and Solutions

Problem 1:

Create a box and whisker plot for the following dataset:

12, 15, 18, 20, 22, 25, 30, 35, 40

Solution:

Box and Whisker Plot:

  +---------------+
  |               |
  |  12  15  18  20|
  |               |
  +---------------+
           |
           |
           v
  +---------------+
  |               |
  |  22  25  30  35|
  |               |
  +---------------+
           |
           |
           v
  +---------------+
  |               |
  |  40          |
  |               |
  +---------------+

Problem 2:

A dataset has a median of 25, Q1 = 15, and Q3 = 35. What is the IQR?

Solution:

IQR = Q3 - Q1 = 35 - 15 = 20

Problem 3:

A box and whisker plot shows a median of 20, Q1 = 10, and Q3 = 30. What is the range of the data?

Solution:

Range = Maximum value - Minimum value Since the whiskers extend to the minimum and maximum values, we can see that the range is approximately 40 - 0 = 40.

📝 Note: The range is an approximate value, as the exact values of the minimum and maximum are not provided.

Conclusion

In this worksheet, we have learned how to read and interpret box and whisker plots, and how to create our own plots. We have also practiced solving problems using box and whisker plots. Remember to always identify the median, quartiles, and IQR when reading a box and whisker plot, and to check for outliers when interpreting the data.

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