[DATA] Bull and Bear Markets The stock market goes through periods known as bull markets and bear markets. A bull market exists when the stock market increases in value by at least 20%, while a bear market exists when the stock market decreases in value by at least 20%. The data below represent the number of months a random sample of bull and bear markets have lasted.


d. Draw a side-by-side boxplot by market condition. Discuss any interesting features of the graph.

Verified step by step guidance

1. Step 1: Organize the data into two groups based on market condition: Bear Months and Bull Months, as given in the table.
2. Step 2: For each group, calculate the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These values are essential for constructing boxplots.
3. Step 3: Draw the boxplot for each group side-by-side on the same scale. Each boxplot should have a box from Q1 to Q3, a line at the median, and whiskers extending to the minimum and maximum values (or to the nearest non-outlier values if you identify outliers).
4. Step 4: Compare the two boxplots by examining their medians, interquartile ranges (IQR = Q3 - Q1), overall range, and any potential outliers. Note differences in central tendency, spread, and skewness between bear and bull market durations.
5. Step 5: Discuss interesting features such as which market tends to last longer, which has more variability, and whether there are any extreme values or outliers that might affect interpretation.

Key Concepts

Boxplot Construction and Interpretation

A boxplot visually summarizes data distribution through five key statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It highlights the central tendency, spread, and potential outliers, making it easier to compare groups side-by-side, such as bear and bull market durations.

Comparing Distributions

Comparing distributions involves analyzing differences in shape, center, spread, and outliers between groups. Side-by-side boxplots allow direct visual comparison of these features, helping to identify which market condition tends to last longer or has more variability.

Understanding Market Conditions and Data Context

Bull and bear markets represent periods of rising and falling stock values, respectively, with durations measured in months. Understanding this context helps interpret the data meaningfully, such as recognizing that longer bull markets might indicate sustained growth phases, while bear markets may be shorter but more volatile.