Question 1

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

Accepted Answer

Mean is the arithmetic average — the sum of all values divided by the count. Median is the middle value when data is sorted; it is less affected by outliers. Mode is the most frequently occurring value. For a symmetric distribution all three are equal. When data is skewed — for example, income distributions with very high earners — the median is a better measure of the "typical" value than the mean.

Question 2

When should I use weighted mean instead of arithmetic mean?

Accepted Answer

Use weighted mean when different values contribute unequally to the result. Common examples: calculating a course GPA where exams count more than quizzes, finding a portfolio return when positions are different sizes, or computing a national average price when regions have different populations. If all weights are equal, weighted mean equals arithmetic mean.

Question 3

What is geometric mean used for?

Accepted Answer

Geometric mean is the correct average for multiplicative processes: compound interest, investment growth rates, population growth, and index numbers. If an investment returned +50% one year and −33% the next, the arithmetic mean suggests +8.5% average return — misleading. The geometric mean gives ≈ +0.25%: √(1.50 × 0.67) − 1 ≈ 0.0025, reflecting that you nearly broke even (ending value ≈ $100.50 on a $100 start). Formula: geometric mean = (x₁ × x₂ × ... × xₙ)^(1/n).

Question 4

Can I calculate the mean with negative numbers?

Accepted Answer

Yes — arithmetic mean works fine with negative numbers. Simply include them in the sum. For example, the mean of {−5, −2, 3, 8} = (−5 + −2 + 3 + 8) / 4 = 4 / 4 = 1. Geometric mean, however, requires all positive values; it is undefined for negative or zero inputs.

Question 5

How does an outlier affect the mean?

Accepted Answer

Outliers disproportionately pull the arithmetic mean toward them. For example, the mean of {10, 11, 12, 13, 100} is 29.2 — far above the four clustered values. The median of the same dataset is 12, which better represents the central group. When your data contains known outliers, report both mean and median, and consider whether to trim or winsorize the outlier before calculating.

Question 6

What is the difference between population mean (μ) and sample mean (x̄)?

Accepted Answer

Population mean (μ) is computed from every member of the group you are studying. Sample mean (x̄) is computed from a subset. The formula is identical (Σx / n), but the interpretation differs: x̄ is an estimate of μ. In inferential statistics, we use x̄ along with standard error to make probability statements about μ. When a dataset represents the entire population, use μ; when it is a sample, use x̄.

Mean Type	Best For	Avoid When
Arithmetic	Test scores, temperatures, heights	Data has extreme outliers
Weighted	GPA, portfolio returns, survey data	All items are equally important
Geometric	Investment CAGR, population growth rates	Data contains zeros or negatives
Harmonic	Average speed, P/E ratios, fuel efficiency	Values are not rates or ratios

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