How do you calculate the average (mean) of a set of numbers?

Add all the numbers together, then divide by the count. Formula: Mean = Sum ÷ Count. Example: (4 + 8 + 6 + 5 + 3) ÷ 5 = 26 ÷ 5 = 5.2.

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

Mean: the arithmetic average (sum ÷ count). Median: the middle value when numbers are sorted. Mode: the value that appears most often. Example set: 2, 3, 3, 5, 7. Mean = 4, Median = 3, Mode = 3.

How do you calculate a weighted average?

Multiply each value by its weight, sum the results, then divide by the total weight. Formula: Weighted Mean = Σ(value × weight) ÷ Σ(weights). Example: grades 80 (weight 3) and 90 (weight 2) → (80×3 + 90×2) ÷ (3+2) = (240+180) ÷ 5 = 84.

How do you find the median of a set of numbers?

Sort the numbers in ascending order. If the count is odd, the median is the middle value. If the count is even, the median is the average of the two middle values. Example (odd): 2, 3, 5, 7, 9 → median = 5. Example (even): 2, 3, 5, 7 → median = (3+5)÷2 = 4.

What is a trimmed mean and when should I use it?

A trimmed mean removes a percentage of the highest and lowest values before calculating the average. This reduces the effect of outliers. Example: 5% trimmed mean of 20 values removes the top and bottom 5% (1 value each) then averages the middle 18. Used in statistics, finance (Olympic judging), and quality control.

How do you calculate the mean from grouped data or a frequency table?

For each class, use the midpoint of the interval as the value. Multiply each midpoint by its frequency. Sum the products and divide by the total frequency. Formula: Mean = Σ(midpoint × frequency) ÷ Σ(frequency).

What is the difference between population standard deviation and sample standard deviation?

Population SD (σ): divide by N. Use when you have data for the entire population. Sample SD (s): divide by N-1 (Bessel's correction). Use when your data is a sample from a larger population — this is the more common case in practice.

What is a moving average and how is it calculated?

A moving average smooths a data series by averaging a fixed window of consecutive values. For a 3-period moving average of [2, 4, 6, 8, 10]: first value = (2+4+6)÷3 = 4, second = (4+6+8)÷3 = 6, third = (6+8+10)÷3 = 8. Used in finance, forecasting, and trend analysis.

How do I calculate the average of percentages?

If all percentages apply to the same base, take a simple arithmetic mean. If they apply to different bases (e.g. conversion rates from different traffic sources), use a weighted average where the weight is the base size. Simple averaging percentages with different bases gives misleading results — always check if weights differ.

Average Calculator – Mean, Median, Mode, Weighted Average & More (Free 2026)

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Mean, Median, Mode & More — Formulas & When to Use Each

Mean, median, and mode are three different ways to describe the "centre" of a dataset. Each tells you something different — and choosing the wrong one can be misleading.

The Three Measures of Central Tendency

Arithmetic Mean (Average)

Mean = Σx ÷ n

Sum all values, divide by count

Example: (2+4+6+8) ÷ 4 = 5

Sensitive to outliers — one extreme value pulls the mean

Median (Middle Value)

Sort → pick middle (or avg of 2 middles)

Odd count: middle value. Even count: avg of two middle values

Example (odd): 2,3,5,7,9 → median = 5

Example (even): 2,3,5,7 → median = (3+5)÷2 = 4

Not affected by outliers — best for skewed data (house prices)

Mode (Most Frequent)

Most frequently occurring value

Can have multiple modes (bimodal, multimodal) or no mode

Example: 2,3,3,5,7 → mode = 3

Best for categorical data (favourite colour, most common size)

Weighted Average

Weighted Mean

Weighted Mean = Σ(xᵢ × wᵢ) ÷ Σ(wᵢ)

Example: Grades 80 (weight 3) and 90 (weight 2)

= (80×3 + 90×2) ÷ (3+2) = 420 ÷ 5 = 84

Standard Deviation

Population vs Sample SD

σ = √[Σ(x−μ)² ÷ N]

Population (σ): divide by N — use when you have all data

Sample (s): divide by N−1 — use when data is a sample

Measures how spread out values are from the mean

When Mean Misleads: House Prices

Prices: $200k, $210k, $220k, $230k, $2,000k

Mean = $572k — misleadingly high due to one mansion

Median = $220k — better represents the typical home

✓ For skewed data with outliers, use median, not mean

Reference Tables

Average & Statistics Quick Reference (2026)

Quick lookup for common statistical measures and when to use each type of average.

Which Average to Use — Decision Guide

Situation	Best Measure	Why	Avoid
House prices / salaries	Median	Outliers (mansions, CEO pay) skew the mean	Mean
Test scores (no outliers)	Mean	Normally distributed, outliers rare	Mode
Most popular shoe size	Mode	Categorical — "most common" is what matters	Mean
Grading with weighted assignments	Weighted mean	Final exam worth more than homework	Simple mean
Stock price trend	Moving average	Smooths daily noise to show trend	Simple mean
Olympic judging	Trimmed mean	Removes highest/lowest scores to prevent bias	Mean
Survey data (Likert scale)	Mean or median	Mean if symmetric; median if skewed responses	Mode only
Grouped/binned data	Grouped mean	Individual values unknown; only frequencies available	Simple mean

Mean vs Median — Example Comparison

Dataset	Mean	Median	Mode	Note
Symmetric: 2,4,6,8,10	6	6	None	Mean ≈ Median
Right-skewed: 2,3,4,5,50	12.8	4	None	Mean skewed by outlier
Repeated: 3,3,5,7,9,9,9	6.43	7	9	Mean ≈ Median
All same: 4,4,4,4,4	4	4	4	Mean ≈ Median
Two modes: 1,2,2,3,4,4,5	3	3	2,4	Mean ≈ Median
No mode: 1,2,3,4,5,6	3.5	3.5	None	Mean ≈ Median
Exam scores: 55,70,72,78,90,95	76.67	75	None	Mean skewed by outlier

Standard Deviation Interpretation

SD relative to mean	Interpretation	Example
Very low (SD < 5% of mean)	Values are tightly clustered around the mean	Factory output with tight tolerances
Low (SD 5–15% of mean)	Moderate consistency	Student test scores in a well-taught class
Moderate (SD 15–30% of mean)	Noticeable spread	Investment returns year-on-year
High (SD > 30% of mean)	High variability; outliers likely	House prices in a mixed neighbourhood
68-95-99.7 rule (normal dist.)	68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD	Heights, IQ scores, measurement errors

FAQ

Average Calculator — Frequently Asked Questions

Everything you need to know about calculating means, weighted averages, medians, modes, and choosing the right measure for your data.

Average Calculator — Mean, Median, Mode, Weighted Average & More (2026)