D3.2.15 Box-and-whisker plots to represent data for a continuous variable such as student height Notes

Using Box-and-Whisker Plots to Visualize Continuous Data

1. It uses five key statistics, along with the identification of outliers:
   1. Minimum: The smallest data value, excluding outliers.
   2. First Quartile (Q1): The median of the lower half of the data.
   3. Median (Q2): The middle value of the dataset.
   4. Third Quartile (Q3): The median of the upper half of the data.
   5. Maximum: The largest data value, excluding outliers.
   6. Outliers: Data points that fall significantly outside the typical range, calculated as more than 1.5 × IQR above Q3 or below Q1.

Why Are Box-and-Whisker Plots Useful?

1. Box-and-whisker plots provide a clear, concise way to:
   1. Summarize Data: Visualize the range, spread, and central tendency of the dataset.
   2. Identify Outliers: Spot unusual data points that lie far from the majority.
   3. Compare Datasets: Use multiple box plots side by side to compare distributions across groups.

How to Create a Box-and-Whisker Plot

Step 1: Organize the Data

Arrange your data values in ascending order.

Step 2: Calculate Key Statistics

1. Find the Median (Q2): Divide the dataset into two equal halves.
2. Find Q1 and Q3: Identify the medians of the lower and upper halves.
3. Calculate the Interquartile Range (IQR): Subtract Q1 from Q3: IQR=Q3−Q1IQR = Q3 - Q1IQR=Q3−Q1

Step 3: Identify Outliers

1. Multiply the IQR by 1.5: 1.5×IQR1.5 \times IQR1.5×IQR
2. Add this value to Q3 to find the upper bound for outliers.
3. Subtract this value from Q1 to find the lower bound for outliers.

Step 4: Draw the Plot

1. Box: Draw a rectangle from Q1 to Q3.
2. Median: Add a line inside the box at Q2.
3. Whiskers: Extend lines from the box to the minimum and maximum values within the non-outlier range.