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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Mean Median Mode Calculator

Mean is the arithmetic average (sum divided by count). Median is the middle value when sorted. Mode is the value that appears most often. For the dataset 3, 7, 7, 2, 9: mean = 5.6, median = 7, mode = 7. Mean is sensitive to outliers; median is resistant to them. This calculator also computes standard deviation, variance, quartiles (Q1, Q3), IQR, range, and the five-number summary.

Calculate mean (average), median (middle value), and mode (most frequent) for any dataset. Also shows standard deviation, variance, range, quartiles (Q1, Q3), IQR, and five-number summary.

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Enter a list of numbers to calculate mean, median, mode, standard deviation, and more.

How to Use

1
Enter your numbers
Type or paste your numbers into the textarea, separated by commas, spaces, or newlines. Use the Presets buttons to load sample datasets (test scores, heights, prices, or a small dataset) for a quick demo.
2
View central tendency
The calculator instantly shows mean (arithmetic average), median (middle value when sorted), and mode (most frequent value). If no value repeats, "No mode" is shown.
3
Check spread and variability
Review range, population standard deviation, sample standard deviation, and variance. Use population std dev when you have all data; use sample std dev when it's a subset of a larger dataset.
4
Read the five-number summary
The summary shows min, Q1 (25th percentile), median, Q3 (75th percentile), and max. The IQR (Q3 - Q1) measures the spread of the middle 50%. Use these for box-and-whisker plots.
5
Copy results
Click Copy to get all statistics (mean, median, mode, std dev, quartiles, range, sum) in one paste-ready block for use in reports or homework.

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.

Mean Median Mode Calculator

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