Mean, Median, Mode Calculator

Calculate central tendency, dispersion, quartiles and detect outliers.

Statistical Analysis Results

Mean — Median — Mode — Variance — Standard Deviation — Q1 (25th percentile) — Q3 (75th percentile) — IQR (Interquartile Range) — Minimum — Maximum — Range — Count —

GUIDE

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Mean and Median - Central Tendency

The mean is the sum of all data divided by count, the most common representative value. However, it can be distorted by extreme values. The median is the middle value when data is sorted, providing a more stable center unaffected by outliers. For example, the mean of 1, 2, 3, 4, 100 is 22, but the median is 3, better reflecting the actual distribution.

Variance and Standard Deviation - Data Spread

Variance measures how far each data point is from the mean. Standard deviation is the square root of variance, having the same unit as the data for easier interpretation. Large standard deviation means data is widely spread around the mean; small means clustered near it. Used to measure volatility in finance and product consistency in quality control.

Quartiles and IQR - Understanding Distribution

Quartiles divide data into four equal parts: Q1 (25%), Q2 (50%, median), Q3 (75%). IQR (Interquartile Range) is Q3 - Q1, showing how spread the middle 50% of data is. IQR is used for outlier detection. Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered outliers.

Outlier Detection - 1.5×IQR Rule

Outliers are values significantly different from other data, possibly due to measurement errors or special events. The most common detection method is the 1.5×IQR rule. Values smaller than Q1 - 1.5×IQR or larger than Q3 + 1.5×IQR are considered outliers. Identifying outliers improves data quality and reveals special patterns.

Histogram - Visualizing Distribution

A histogram divides data into bins and displays the frequency of each bin as bars. It reveals the distribution shape (normal, skewness, kurtosis) at a glance. Symmetric bell shape indicates normal distribution; skewed shape indicates biased distribution. Histograms easily show mode intervals, distribution patterns, and outliers.

Box Plot - Five Key Statistics

A box plot displays five statistics in one graph: minimum, Q1, median (Q2), Q3, maximum. The box represents IQR (Q1~Q3), the line inside shows median, and whiskers show normal range. Points outside whiskers are outliers. Very useful for comparing multiple groups or determining distribution symmetry.

Frequently asked questions

Should I use the mean or the median?

The mean works well when there are no extreme outliers, but for skewed data like income, the median is more representative of the typical value. A large gap between them signals an asymmetric distribution.

Can there be more than one mode, or no mode at all?

Yes. If multiple values share the highest frequency, the data is multimodal, and if every value appears only once, there is no mode. The calculator will show whichever applies to your data.

How should I format my input data?

Enter numbers separated by commas or spaces. Decimals and negative numbers are supported, and there is no strict limit on how many values you can enter.

Do I need to remove values flagged as outliers by the IQR rule?

Not necessarily. The 1.5×IQR rule is just a common guideline — whether a flagged value is a measurement error or a genuinely meaningful data point depends on the context of your data.

Should I use variance or standard deviation?

Standard deviation is usually more useful since it shares the same unit as your original data, making it easier to interpret. Variance is mainly an intermediate step used in further statistical calculations.