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Mean, Median, Mode Explained
What is the difference between mean, median and mode?+
Mean = sum divided by count. Sensitive to outliers. Median = middle value when sorted. Robust to outliers — often used for income data. Mode = most frequently occurring value. Useful for categorical data. Example: {1, 2, 2, 3, 100} — Mean = 21.6, Median = 2, Mode = 2. Median and mode better represent this dataset than the mean.
When should I use median instead of mean?+
Use median when your data has outliers or is skewed. Median income is preferred over mean income because a small number of very high earners pull the mean up significantly. Home prices, response times, and salary data are also typically reported using the median. Use mean when data is roughly symmetrical with no extreme outliers.
What is standard deviation?+
Standard deviation measures how spread out the numbers are from the mean. A low standard deviation means values cluster closely around the mean. A high standard deviation means they are spread out. Formula: square root of the average of squared differences from the mean. We calculate the population standard deviation (dividing by n, not n-1).
What is the geometric mean?+
The geometric mean is the nth root of the product of n numbers. For {2, 8}: geometric mean = √(2×8) = √16 = 4. Unlike the arithmetic mean, the geometric mean is ideal for data that grows multiplicatively — like investment returns, population growth, or ratios. Example: 20% return then 80% return has an arithmetic mean of 50% but geometric mean (actual average growth) of only 20%.