Descriptive statistics summarize and organize characteristics of a data set to reveal underlying patterns.
1. Mean vs. Median in Skewed Data
Mean (μ or x̄): Sum of all values divided by count n. Highly sensitive to extreme outlier spikes (e.g. billionaire incomes skewing average neighborhood salaries).
Median (Q2): The middle value when sorted. Robust against outliers, which is why economists prefer median household income over mean income.
Mode: The value that appears with the highest frequency in the dataset.
2. Identifying Outliers Using the 1.5 × IQR Rule
Statisticians define mild outliers as any observation falling outside:
Always report the median when dealing with heavily skewed distributions (such as real estate house prices or wealth), because a single multi-million dollar mansion distorts the arithmetic mean but has minimal impact on the median.
Yes. If two different numbers share the highest frequency, the distribution is bimodal. If three or more tie, it is multimodal. If every number appears exactly once, there is no mode.
When sample size n is even, there is no single middle number. The median is the average of the two middle numbers: Median = (x_{n/2} + x_{n/2 + 1}) / 2.