Mean Median Mode Range Calculator
Calculate mean, median, mode, and range from a data set with step-by-step work. Enter values for instant results with step-by-step formulas.
Formula
Mean = Σx / n | Median = middle value | Mode = most frequent
Mean is the sum of all values divided by count. Median is the middle value in sorted data (average of two middle values for even counts). Mode is the value that appears most frequently. Range is the difference between maximum and minimum values.
Worked Examples
Example 1: Student Test Scores
Problem: Find the mean, median, mode, and range of these test scores: 85, 92, 78, 90, 85, 88, 76, 95, 85, 82
Solution: Sorted: 76, 78, 82, 85, 85, 85, 88, 90, 92, 95\nMean = 856 / 10 = 85.6\nMedian = (85 + 88) / 2 = 86.5\nMode = 85 (appears 3 times)\nRange = 95 - 76 = 19
Result: Mean: 85.6 | Median: 86.5 | Mode: 85 | Range: 19
Example 2: Daily Temperatures
Problem: Analyze these temperatures (°F): 72, 68, 75, 71, 69, 73, 70
Solution: Sorted: 68, 69, 70, 71, 72, 73, 75\nMean = 498 / 7 = 71.14\nMedian = 71 (middle value)\nMode = No mode (all unique)\nRange = 75 - 68 = 7\nStd Dev = 2.27
Result: Mean: 71.14 | Median: 71 | Mode: None | Range: 7
Frequently Asked Questions
What is the difference between mean, median, and mode?
The mean (average) is the sum of all values divided by the count. The median is the middle value when data is sorted — it splits the data into two equal halves. The mode is the most frequently occurring value. For symmetric distributions, mean ≈ median ≈ mode. For skewed distributions they differ: in right-skewed data, mean > median > mode; in left-skewed data, mean < median < mode. The median is more robust to outliers than the mean.
When should I use the median instead of the mean?
Use the median when your data has outliers or is skewed. For example, income data: if 9 people earn $50K and 1 earns $5M, the mean is $545K (misleading), but the median is $50K (representative). The median is also preferred for ordinal data, house prices, response times, and any dataset where extreme values could distort the average. Use the mean when data is roughly symmetric and you need to include all values in the measure.
Can a dataset have more than one mode?
Yes. A dataset is unimodal if it has one mode (e.g., 1,2,2,3 — mode is 2), bimodal if it has two modes (e.g., 1,2,2,3,3,4 — modes are 2 and 3), and multimodal if it has more than two. If all values occur with equal frequency, there is no mode. Mode is the only measure of central tendency that works for categorical (non-numeric) data, such as favorite colors or brands.
What does range tell us about data?
Range = Maximum - Minimum. It measures the total spread of the data. A larger range indicates more variability. However, range is very sensitive to outliers since it only uses the two most extreme values. For example, the data set {10, 12, 11, 13, 100} has a range of 90, driven entirely by the outlier 100. Standard deviation and interquartile range (IQR) are more robust measures of spread.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
What formula does Mean Median Mode Range Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.