Mean, Median, Mode Calculator – Average, Middle & Most Frequent Value | CalcVelo
📊 Statistics Tool · 7 Measures at Once
Mean, Median, Mode Calculator
Find mean, median, mode, range, variance, and standard deviation instantly — with step-by-step solutions, frequency chart, outlier detection, and skewness indicator.
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Enter Your Data
Separate numbers with commas, spaces, or new lines — paste from Excel too
💡 Accepts: commas, spaces, new lines, or mixed — any format works
Examples:
Mean (Average)
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Median
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Mode
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Range
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Count (n)
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Sum (Σ)
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Std Dev (σ)
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Variance (σ²)
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📋 Sorted Data (🟢 = mode, 🔴 = outlier)
📊 Frequency Distribution
How to Find Mean, Median, and Mode
Mean, median, and mode are the three measures of central tendency in statistics. They describe where the center of a dataset lies, each from a different perspective.
Mean Formula (Average)
Mean = (Sum of all values) ÷ (Number of values)
Example: {2,4,6,8,10} → Mean = 30 ÷ 5 = 6
Median Formula (Middle Value)
Odd count: Median = middle value after sorting
Even count: Median = average of two middle values
Example: {1,3,5,7,9} → Median = 5
Mode Formula (Most Frequent)
Mode = value(s) that appear most often
Example: {2,3,3,4,5,5,5} → Mode = 5 (appears 3 times)
When to Use Mean vs Median vs Mode
Use Mean: Symmetric data without outliers — test scores, heights, temperatures
Use Median: Skewed data or when outliers exist — house prices, salaries, income
Use Mode: Categorical data, shoe sizes, most popular item, most common response
What is Standard Deviation?
Standard deviation (σ) measures how spread out values are from the mean. A low σ means data is tightly clustered; a high σ means widely spread. Formula: σ = √(Σ(x-mean)² / n).
What are Outliers?
Outliers are values that lie far from the rest of the data. This calculator uses the IQR method: values below Q1−1.5×IQR or above Q3+1.5×IQR are flagged as outliers (shown in red).
Mean, Median, Mode — Real World Examples
Test scores {70,80,85,90,95}: Mean=84, Median=85 — symmetric data, both similar
Salaries {20k,22k,25k,28k,200k}: Mean=59k, Median=25k — outlier pulls mean up, use median
Shoe sizes {7,8,8,9,9,9,10}: Mode=9 — most useful for inventory decisions
Temperature {10,12,11,13,12,12}: Mode=12°C — most common temperature of the week
What is Skewness?
Skewness describes the asymmetry of a distribution:
Symmetric: Mean ≈ Median — data is balanced (e.g. heights in a population)
Positive Skew: Mean > Median — long tail on the right, high outliers exist (e.g. income data)
Negative Skew: Mean < Median — long tail on the left, low outliers exist (e.g. exam scores when most do well)
Population vs Sample Standard Deviation
This calculator uses population standard deviation (σ) — divide by n. If your data is a sample from a larger population, use sample standard deviation (s) — divide by n−1. For most homework and school problems, population std dev is correct.
How to Find Mean Median Mode — Quick Reference
Mean = Σx / n | Median = middle value (sorted) | Mode = most frequent
Range = Max − Min | Variance = Σ(x−mean)² / n | Std Dev = √Variance
The mean is the arithmetic average — add all values and divide by count. Example: {2,4,6,8,10} → Sum=30, Count=5, Mean=6. The mean is sensitive to outliers — one extreme value can significantly shift it upward or downward.
The median is the middle value when sorted. For odd count: it's the middle value. For even count: it's the average of the two middle values. Use median for skewed data or when outliers exist — for example, median household income is more informative than mean income because a few billionaires don't skew it.
Yes. A dataset can have no mode (all values appear equally), one mode (unimodal), two modes (bimodal), or more (multimodal). Example: {1,2,2,3,3,4} has two modes: 2 and 3. This calculator identifies all modes including multimodal datasets.
Mean = arithmetic average (add all, divide by count). Median = middle value when sorted. Mode = most frequent value. For symmetric distributions, all three are equal. When data is skewed, they differ — mean is pulled toward the tail, while median remains more central.
Standard deviation (σ) measures how much values deviate from the mean on average. A small σ means data is tightly clustered around the mean. A large σ means data is widely spread. Example: {5,5,5,5} has σ=0. {1,5,5,9} has a larger σ because values are more spread.
For grouped data, use class midpoints × frequencies for mean. For median, use the cumulative frequency formula. For mode, the modal class is the one with the highest frequency. This calculator works with individual (ungrouped) data — enter each value separately.
An outlier is a value that lies far from the rest of the data. This calculator uses the IQR method: Q1 - 1.5×IQR and Q3 + 1.5×IQR. Values outside this range are flagged as outliers (shown in red). Outliers significantly affect the mean but not the median — which is why median is preferred for skewed datasets.
CalcVelo Mean, Median, Mode Calculator — Free online statistics tool. Find mean, median, mode, range, variance, standard deviation with step-by-step solutions, frequency chart, outlier detection, and skewness indicator.
