Calculate mean, median, mode, and range
Statistical averages help summarize and understand data sets. The most common measures are mean (arithmetic average), median (middle value), and mode (most frequent value). Each provides different insights into your data's central tendency.
Mean = Sum of all values / Number of values
| Calculation | Expression | Result |
|---|---|---|
| Mean of numbers | 10, 20, 30, 40, 50 | Mean: 30 |
| Median of numbers | 1, 3, 5, 7, 9 | Median: 5 |
| Mode of numbers | 1, 2, 2, 3, 4 | Mode: 2 |
| Range of numbers | 5, 10, 15, 20 | Range: 15 |
Mean is the arithmetic average (sum divided by count). Median is the middle value when data is sorted. Mode is the most frequently occurring value. For example, in [1, 2, 2, 3, 10]: mean = 3.6, median = 2, mode = 2. Each is useful in different situations.
Use median when your data has outliers or is skewed. For example, income data often uses median because a few very high incomes would make the mean misleadingly high. Median represents the typical value more accurately in such cases.
Standard deviation measures how spread out numbers are from the mean. A low standard deviation means values cluster near the mean; a high one means they're spread out. It's calculated as the square root of variance (average of squared differences from the mean).
Range is the difference between the largest and smallest values in a data set. It provides a quick measure of data spread but is sensitive to outliers. For example, in [2, 5, 8, 12, 15], the range is 15 - 2 = 13.
When you have an even number of values, the median is the average of the two middle numbers. For example, in [1, 3, 5, 7], the two middle values are 3 and 5, so the median is (3 + 5) / 2 = 4.
A weighted average assigns different importance (weights) to different values. Multiply each value by its weight, sum the products, and divide by the sum of weights. Common in calculating grades where different assignments have different point values.