What is the average of 5 numbers?

Add all five numbers and divide by 5. For 10, 20, 30, 40, 50: sum = 150, average = 150 ÷ 5 = 30. This is the arithmetic mean. Enter the numbers separated by commas and press Calculate to get the mean instantly.

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

Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. Mode is the most frequent value. For skewed data (income, house prices), median is more representative. For symmetric data, all three are similar.

How do I calculate a weighted average?

Switch to the Weighted Average tab. Enter each value and its weight. Weighted mean = Σ(value × weight) / Σ(weights). Example: exam scores 80 (weight 30%), 90 (weight 70%) = (80×0.3 + 90×0.7) / 1 = 87.

What is standard deviation and how is it different from variance?

Variance is the average squared deviation from the mean. Standard deviation is the square root of variance — it is in the same units as the data, making it easier to interpret. Sample SD divides by (n−1); population SD divides by n.

What are Q1, Q2, Q3 and IQR?

Q1 (25th percentile), Q2 (median, 50th), Q3 (75th percentile). IQR = Q3 − Q1. The IQR covers the middle 50% of data. Outliers are values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR (Tukey fence method).

When should I use mean vs median?

Use mean when data is symmetric without extreme outliers. Use median when data is skewed or has outliers — a few very high values pull the mean up but do not affect the median. Income and house prices always use median for this reason.

How do I enter numbers into the calculator?

Type numbers separated by commas, spaces, or new lines — all three formats work. Example: 10, 20, 30, 40 or 10 20 30 40. Negative numbers and decimals are supported. The calculator accepts up to hundreds of values.

Average Calculator

Calculate mean, median, mode, range, standard deviation, quartiles, and outliers. Three modes: descriptive statistics, weighted average, and frequency table.

Dataset (comma, space, or newline separated)

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Guides & Reference

How It Works

Descriptive Stats — full summaryAnalyzing any dataset: grades, measurements, survey results.

Enter numbers separated by commas or spaces. The calculator computes: count, sum, mean, median, mode (flags "No mode" if all values are unique), min, max, range, midrange, population SD, sample SD, population variance, sample variance, Q1, Q2, Q3, IQR, skewness, kurtosis, CV%, and outliers using the Tukey 1.5×IQR fence. A histogram also renders for visual distribution.

Mean = Σx / n | SD = √(Σ(x−mean)² / (n−1)) | IQR = Q3 − Q1

Input: 4,8,15,16,23,42 → Mean=18, Median=15.5, SD=14.08

Weighted Average tabGPA, course grades, financial returns, survey weights.

Each value gets a weight. Weighted mean = Σ(value × weight) / Σ(weights). Weights do not need to sum to 1 or 100 — the calculator normalizes automatically. Enter grade 90 weight 3, grade 80 weight 1: weighted mean = (90×3 + 80×1) / 4 = 350/4 = 87.5. Unweighted mean of 90 and 80 would be 85 — the difference shows the impact of weighting.

Weighted mean = Σ(xᵢ × wᵢ) / Σ(wᵢ)

Physics 85 (4cr), Math 90 (3cr), History 78 (2cr) → WA = 85.1

Frequency Table tabGrouped data, large surveys, repeated values.

Enter each unique value and its frequency count instead of listing every individual value. Example: a class where 5 students scored 70, 12 scored 80, 8 scored 90. Enter value 70 frequency 5, value 80 frequency 12, value 90 frequency 8. The calculator computes the mean and full stats as if all 25 individual scores were entered.

Mean = Σ(value × frequency) / Σ(frequencies)

70×5 + 80×12 + 90×8 = 2090 / 25 = 83.6

Outlier detection — Tukey fencesData quality checks, removing bad measurements, identifying anomalies.

The calculator flags outliers using the Tukey method: lower fence = Q1 − 1.5×IQR, upper fence = Q3 + 1.5×IQR. Any value outside these fences is listed as an outlier. Example: dataset 2, 3, 4, 5, 6, 100 — value 100 is an outlier (far above the upper fence). Outliers are listed in the results so you can decide whether to investigate or exclude them.

Outlier if: x < Q1 − 1.5×IQR or x > Q3 + 1.5×IQR

Data: 2,3,4,5,6,100 → outlier detected: 100

Skewness and kurtosisUnderstanding distribution shape for statistics and data science.

Skewness measures distribution asymmetry: positive = right tail longer (mean > median), negative = left tail longer. Kurtosis measures peak sharpness vs a normal distribution: excess kurtosis > 0 means heavier tails (leptokurtic), < 0 means lighter tails (platykurtic). Both use sample-corrected formulas (n ≥ 3 required for meaningful results).

Skewness: γ₁ = n/((n−1)(n−2)) × Σ((xᵢ−x̄)/s)³

Right-skewed income data: positive skewness, mean > median

Quick Reference

Common calculations — verify these in the calculator above.

Descriptive

Mean of 4,8,15,16,23,42

Descriptive

Median of 1,2,2,3,100

Descriptive

Mode of 1,2,2,3,3,3

Sample SD

SD of 2,4,4,4,5,5,7,9

Weighted

WA: 90(w=3), 80(w=1)

87.5

Quartiles

IQR of 1,2,3,4,5,6,7

Descriptive

Range of 5,10,15,20,25

Descriptive

Mean of 100,100,100,200

125

Tips & Shortcuts

✓

Paste a column directly from Excel or Google Sheets — the calculator handles newline-separated values the same as comma-separated ones. No reformatting needed.

✓

For weighted GPA, use credit hours as weights. The result automatically accounts for 4-credit courses having more influence than 1-credit courses.

✓

If mean and median differ significantly, check the outlier list — a single extreme value can pull the mean far from where most data sits.

✓

The Coefficient of Variation (CV%) in the results lets you compare spread across datasets with different units or scales. CV = SD / mean × 100.

✓

For frequency table data, enter totals instead of individual values: "score 85, count 12" is faster than listing 85 twelve times and gives identical results.

Common Mistakes

Using mean for skewed data like income or house prices

A few billionaires in a dataset raise the mean dramatically while the median stays near the typical person. Always use median for right-skewed distributions. The calculator shows both — compare them to detect skew.

Using population SD when the data is a sample

Sample SD (divides by n−1) is almost always correct. Population SD (divides by n) is only valid when you have every possible value in the universe of interest — rare in practice. The calculator shows both; use sample SD by default.

Expecting mode to always exist

If all values appear exactly once, there is no mode. The calculator correctly reports "No mode" in this case. A dataset can also be bimodal (two modes) or multimodal — all are listed.

Confusing standard deviation with range as a measure of spread

Range = max − min and is sensitive to a single extreme value. Standard deviation uses all data points and is a more robust measure of typical spread. IQR (Q3−Q1) is even more robust, ignoring the top and bottom 25% entirely.

Entering numbers with units or symbols (e.g. $50, 30%)

Remove units before entering. The calculator accepts only numbers — entering "$50" causes a parse error. Strip dollar signs, percent signs, and commas from thousand separators (use 1000 not 1,000).

Frequently Asked Questions

Average (arithmetic mean) = sum of all values ÷ count. For 4, 8, 15, 16, 23, 42: sum = 108, count = 6, mean = 108 ÷ 6 = 18. This calculator also shows median, mode, standard deviation, quartiles, and outliers — all from the same input.

Mean: arithmetic average — sensitive to outliers. Median: middle value when sorted — resistant to outliers. Mode: most frequent value — can have multiple modes or none. For 1, 2, 2, 3, 100: mean = 21.6 (pulled up by 100), median = 2 (unaffected), mode = 2. Use median when data is skewed.

Weighted average = Σ(value × weight) / Σ(weights). Enter each value and assign it a weight. Example: GPA with 3 courses: Physics 85 (4 credits), Math 90 (3 credits), History 78 (2 credits). Weighted GPA = (85×4 + 90×3 + 78×2) / (4+3+2) = (340+270+156)/9 = 766/9 ≈ 85.1.

Standard deviation measures the average distance from the mean. Sample SD (divides by n−1): use when your data is a sample from a larger population — this corrects for bias. Population SD (divides by n): use only when you have every value in the entire population. In practice, sample SD is almost always the right choice.

Q1 (25th percentile) and Q3 (75th percentile) divide the sorted data into quarters. IQR = Q3 − Q1 covers the middle 50% of values. Outlier fences: lower = Q1 − 1.5×IQR, upper = Q3 + 1.5×IQR. Values outside these fences are flagged as outliers by the Tukey method, which this calculator uses automatically.

Use mean for symmetric data without extreme outliers (heights, test scores in a class). Use median for skewed data or when outliers exist (income, house prices, response times). A useful rule: if the mean and median differ by more than 10%, the data is skewed enough that median is the better summary statistic.

Separate numbers with commas, spaces, or new lines — all work interchangeably. Examples: "10, 20, 30" or "10 20 30" or paste a column from a spreadsheet. Negatives (−5) and decimals (3.14) are supported. The Frequency Table tab accepts values with repetition counts for large grouped datasets.

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