Mean Median Mode Calculator

Frequently Asked Questions

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

Mean is the arithmetic average: sum all values and divide by count. Median is the middle value when data is sorted (or the average of the two middle values for even-count datasets). Mode is the value that appears most frequently. For the dataset 2, 3, 7, 7, 9: mean = 5.6, median = 7, mode = 7. Mean is affected by outliers, median is resistant to outliers, and mode identifies the most common value.

When should I use mean vs. median?

Use mean for symmetric, normally distributed data without extreme outliers (test scores, heights). Use median when data is skewed or has outliers (income, house prices, response times). Example: incomes of $40K, $45K, $50K, $55K, $500K — mean = $138K (misleading), median = $50K (representative). In general, if mean and median differ significantly, the data is skewed and the median better represents the "typical" value.

What if there is no mode or multiple modes?

If no value repeats, the dataset has no mode. If two values tie for highest frequency, the dataset is bimodal (two modes). Three or more tied values make it multimodal. Example: 1, 2, 3, 4 has no mode. 1, 2, 2, 3, 3 is bimodal (modes: 2 and 3). A dataset where every value appears equally often is sometimes called "no mode" or "all values are modes." This calculator handles all cases.

What is the five-number summary?

The five-number summary consists of: minimum, Q1 (25th percentile), median (50th percentile), Q3 (75th percentile), and maximum. It describes the spread and shape of a dataset. The interquartile range (IQR = Q3 - Q1) measures the spread of the middle 50% of data. Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered potential outliers in a box plot.

What is the difference between population and sample standard deviation?

Population standard deviation (σ) divides by N (total count): σ = sqrt(Σ(x - μ)² / N). Sample standard deviation (s) divides by N-1: s = sqrt(Σ(x - x̄)² / (N-1)). The N-1 correction (Bessel's correction) compensates for the fact that a sample underestimates the population variance. Use population σ when you have data for the entire group. Use sample s when your data is a subset of a larger population (which is most real-world scenarios).

How do I calculate the mean for grouped or weighted data?

For weighted mean: multiply each value by its weight, sum the products, then divide by the sum of weights. Formula: weighted mean = Σ(value × weight) / Σ(weight). Example: test scores weighted 20%, 30%, 50% for scores 80, 90, 70: (80×0.2 + 90×0.3 + 70×0.5) / 1.0 = 78. This is different from the simple mean of 80 which would treat all scores equally.

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