Compute mean, median, mode, range, variance, and standard deviation for any numerical dataset. Visualize data distribution with an interactive scatter plot.
In statistics, the mean (or arithmetic average) is the most widely used measure of central tendency. It represents the balance point of a dataset, calculated by summing all values and dividing by the number of observations. Alongside the median and mode, the mean provides a concise summary of a distribution's center. However, each measure has distinct strengths and weaknesses depending on the data's shape and the presence of outliers.
\[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \]
The sample mean is the sum of all observations divided by the sample size n.
When you enter a dataset, the calculator parses the values using the selected delimiter (or auto-detects commas, spaces, and newlines). It then computes:
The interactive chart maps each data point on a scatter plot with the mean and median marked as horizontal lines. The shaded bands represent ±1 standard deviation from the mean, giving a visual sense of data spread.
A university instructor enters the final exam scores of 40 students: 52, 58, 61, 64, 67, 68, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 100, 100, 100, 100, 100. The calculator returns a mean of 84.2, a median of 86.5, and a mode of 100. The chart shows a left‑skewed distribution with a cluster of perfect scores pulling the mean slightly lower than the median. The instructor can immediately identify that while the average is high, the median better represents the typical student performance, and the mode highlights the most frequent outcome.
This analysis helps with grade normalization, identifying at‑risk students, and communicating class performance to stakeholders.
A property analyst evaluates home prices in a neighborhood: $250k, $275k, $290k, $310k, $325k, $340k, $360k, $390k, $430k, $510k, $620k, $1.2M. The mean is heavily influenced by the $1.2M mansion, coming in at ~$445k, while the median (~$365k) better represents the typical home price. The chart clearly shows the outlier, and the standard deviation (~$270k) quantifies the high variability. This insight helps the analyst advise buyers and sellers on realistic market expectations.
| Measure | Best Used When | Sensitive to Outliers? | Example |
|---|---|---|---|
| Mean | Data is symmetric and roughly normal; you need the "average" value. | Yes — highly influenced by extreme values. | Heights of adult males in a population. |
| Median | Data is skewed or contains outliers; you want the "typical" value. | No — robust to extreme values. | Household income, home prices. |
| Mode | Data is categorical or you need the most frequent value. | No — depends only on frequency. | Most common shoe size, preferred product color. |
While the mean locates the center of a distribution, standard deviation and variance describe how spread out the data is. A low standard deviation indicates that data points tend to be close to the mean, while a high standard deviation suggests wide dispersion. In many fields — from finance (risk assessment) to quality control (process capability) — these measures are as important as the mean itself. The calculator's ±1 standard deviation bands on the chart provide an intuitive visualization of this spread.
The variance is the average of squared differences from the mean. It is expressed in squared units, which makes interpretation less intuitive, but it is a fundamental building block for many statistical tests and models. The standard deviation, being the square root of variance, returns to the original units and is often preferred for reporting.