How do you calculate the average (mean)?

The arithmetic mean (average) = Sum of all values ÷ Count of values. Example: for the numbers 4, 7, 10, 15, 24: Sum = 60, Count = 5, Mean = 60 ÷ 5 = 12. The mean is the most common measure of central tendency, but it can be skewed by extreme values (outliers).

What is the difference between mean, median, and mode?

Mean (average): sum divided by count — affected by outliers. Median: the middle value when sorted — resistant to outliers. Mode: the most frequent value(s) — useful for categorical data. Example dataset [1, 2, 2, 3, 100]: Mean = 21.6 (skewed by 100), Median = 2 (middle value), Mode = 2 (appears twice). For income data, median is more meaningful than mean because a few billionaires inflate the average.

What is standard deviation and why does it matter?

Standard deviation measures how spread out values are from the mean. A small SD means values cluster tightly around the mean; a large SD means they're spread far apart. Example: test scores [85, 87, 88, 89, 91] have mean=88 and SD≈2.2 (tight cluster). Scores [40, 65, 88, 100, 100] have mean=78.6 and SD≈23.8 (very spread). SD is critical in statistics, finance (volatility), quality control, and scientific research.