Average & Median Calculator

How this is calculated

Mean is the sum of all values divided by the count. Median is the middle value once the list is sorted. Mode is the most frequently occurring value. Range is the highest value minus the lowest.

Mean vs. median vs. mode

These three measures of "central tendency" can tell very different stories about the same data set, especially when outliers are present.

Formulas

Example: for 4, 8, 6, 5, 3, 8, 9 — mean ≈ 6.14, median = 6, mode = 8, range = 6 (from 3 to 9).

Quick reference table

Common pitfalls

• Forgetting to sort before finding the median — the median only works correctly on data sorted from smallest to largest.
• Letting outliers dominate the average — as shown above, a single extreme value can pull the mean far from what "typical" looks like, while the median stays stable.
• Assuming every data set has exactly one mode — some sets have no repeated values (no mode) and others have several equally frequent values (multiple modes).

Tips

• When a data set is roughly symmetric with no major outliers, mean and median tend to be close together.
• Range is a quick, rough measure of spread — standard deviation gives a more complete picture for further analysis.

Frequently asked questions

How do you calculate the average (mean)? Add all the numbers together, then divide by how many numbers there are. The average of 4, 8, and 6 is (4+8+6)/3 = 6.

How do you find the median? Sort the numbers from smallest to largest. If there's an odd count, the median is the middle value; if even, it's the average of the two middle values.

What is the mode? The mode is the value (or values) that appear most often in a data set. A set can have one mode, multiple modes, or no mode if every value is unique.

When should you use median instead of average? Median is more useful than average when a data set has extreme outliers, since a few very high or very low values can skew the average but not the median.

What is the range of a data set? Range is the difference between the largest and smallest values in a data set, giving a quick sense of how spread out the data is.

Worked examples

Example 1 — Test scores: 85, 90, 78, 92, 88 → mean = 86.6, median = 88, range = 14.

Example 2 — Odd number of values: 4, 8, 6, 5, 3, 8, 9 → sorted: 3,4,5,6,8,8,9 → median = 6, mode = 8.

Example 3 — With an outlier: 1, 2, 3, 4, 100 → mean = 22, median = 3 — the median better reflects the "typical" value here.