Overview
This lecture explains how to construct box and whisker plots, including identifying key data points, calculating quartiles, detecting outliers, and plotting the results.
Identifying Key Points for Box and Whisker Plots
- Five key data points: minimum, maximum, first quartile (Q1), second quartile (Q2/median), and third quartile (Q3).
- Arrange the data in ascending order before finding quartiles.
- The median (Q2) divides the dataset into two equal halves.
- Q1 is the median of the lower half; Q3 is the median of the upper half.
- The minimum and maximum are simply the smallest and largest values in the data.
Calculating and Using Quartiles
- For odd-sized datasets, the median is the middle value after sorting.
- For even-sized halves, the quartile is the average of the two middle values in each half.
- Example: Q1 is the average of the 6th and 7th smallest values in a 13-value dataset.
Detecting Outliers
- Interquartile Range (IQR) = Q3 - Q1.
- Outlier boundaries: Q1 - 1.5 × IQR (lower), Q3 + 1.5 × IQR (upper).
- If the minimum or maximum falls outside these boundaries, they are outliers.
Constructing the Box and Whisker Plot
- Draw a number line covering the minimum to the maximum data value.
- Mark and draw a box from Q1 to Q3 with a line at Q2.
- Whiskers extend from the box to the minimum and maximum values (unless outliers exist).
- Plot outliers as separate points beyond the whiskers.
Box Plot Example with Outliers
- If data has an outlier, exclude it from the whiskers and show it as a separate point.
- The max whisker is at the highest non-outlier value; the outlier stands alone.
Key Terms & Definitions
- Box and Whisker Plot — a graphical summary showing the distribution of a dataset using five-number summary.
- Quartile (Q1, Q2, Q3) — values that divide the dataset into four equal parts.
- Median (Q2) — middle value of a sorted dataset.
- Interquartile Range (IQR) — difference between Q3 and Q1; measures the spread of the middle half of data.
- Outlier — a data value outside 1.5 × IQR from the nearest quartile.
Action Items / Next Steps
- Practice arranging datasets, finding quartiles, and identifying outliers.
- Draw box and whisker plots using new data sets for additional practice.