Mean Median Mode Calculator
Find mean (average), median (middle), and mode (most common) from a list of numbers or from a frequency table (value + count). Includes steps, quick picks, and a mini distribution visual.
Background
Mean, median, and mode are three common ways to describe a dataset’s “center.” The mean uses all values (sensitive to outliers), the median is the middle value when sorted (robust to outliers), and the mode is the most frequent value (can be none or multiple).
How to use this calculator
- Choose List or Frequency table.
- Enter your data (paste numbers or pairs like value:frequency).
- Click Calculate to get mean, median, mode, plus optional outliers, spread, and histogram.
How this calculator works
- Mean: sum of values divided by count.
- Median: the middle value(s) after sorting (or the middle position in a frequency table).
- Mode: the most frequent value(s). There may be none or multiple modes.
- Skew (quick hint): mean > median suggests right-skew; mean < median suggests left-skew.
Formula & Equation Used
Mean: x̄ = (Σx)/n
Median (odd n): middle value after sorting
Median (even n): average of the 2 middle values
Mode: value(s) with maximum frequency
Example Problem & Step-by-Step Solution
Example 1 — List input
Dataset: 7, 3, 3, 10, 12
- Sort: 3, 3, 7, 10, 12
- Mean: (7+3+3+10+12)/5 = 35/5 = 7
- Median: the middle value is 7
- Mode: 3 occurs most often → mode is 3
Example 2 — Frequency table
Values: 5:3, 6:1, 7:2
- Total count: n = 3+1+2 = 6
- Mean: (5·3 + 6·1 + 7·2)/6 = (15+6+14)/6 = 35/6 ≈ 5.833
- Median: positions 3 and 4 → median is (5+6)/2 = 5.5
- Mode: max frequency is 3 at value 5 → mode is 5
Example 3 — Outlier effect (mean vs median)
Dataset: 2, 2, 2, 3, 100
- Sort: 2, 2, 2, 3, 100
- Mean: (2+2+2+3+100)/5 = 109/5 = 21.8
- Median: middle value is 2
- Mode: 2 occurs most often → mode is 2
- Takeaway: the outlier (100) pulls the mean far above the median.
Frequently Asked Questions
Q: Can there be more than one mode?
Yes. If two or more values share the same highest frequency, the dataset is multimodal.
Q: What if all numbers occur the same number of times?
Then there’s no mode (no value is more frequent than the others).
Q: Why is the mean different from the median?
Outliers pull the mean. The median is based only on position after sorting, so it’s less affected by extreme values.