The short answer
Mean is the arithmetic average (sum ÷ count), median is the middle value when sorted, mode is the most frequent value, and range is the largest value minus the smallest. Together they summarize a data set from four angles — where it's centered (mean, median, mode) and how spread out it is (range).
Key takeaways
- Mean and median usually sit close together for symmetric data but diverge sharply once outliers or skew enter the picture.
- A data set can have zero modes (all unique values), one mode, or several (bimodal/multimodal) — mode is the only one of the four that can be undefined.
- Range only looks at the two extreme values, so a single outlier can make the spread look much bigger than it really is for the bulk of the data.
- The interquartile range (Q3 − Q1) is a more robust measure of spread than range, since it ignores the most extreme 25% on each end.
The four measures at a glance
| Measure | What it tells you | Sensitive to outliers? |
|---|---|---|
| Mean | Arithmetic center of the data | Yes — shifts with every value |
| Median | Middle value when sorted | No — resistant to extremes |
| Mode | Most frequent value(s) | No — unaffected by extreme values |
| Range | Spread from lowest to highest | Yes — defined entirely by the extremes |
Worked example: one data set, four numbers
Data: 12, 15, 12, 18, 20, 12, 25 — sorted: 12, 12, 12, 15, 18, 20, 25
| Mean | (12+15+12+18+20+12+25) ÷ 7 ≈ 16.29 |
| Median | 4th value in sorted list = 15 |
| Mode | 12 (appears 3 times) |
| Range | 25 − 12 = 13 |
Notice mean (16.29) sits above the median (15) here, pulled upward by 25 — a mild sign of right skew even in a small data set.
Using the IQR to spot outliers
Continuing the same data set (12, 12, 12, 15, 18, 20, 25): splitting around the median gives a lower half of 12, 12, 12 and an upper half of 18, 20, 25. One common method takes the median of each half: Q1 = 12 and Q3 = 20.
IQR = Q3 − Q1 = 20 − 12 = 8
Lower bound = Q1 − 1.5×IQR = 12 − 12 = 0
Upper bound = Q3 + 1.5×IQR = 20 + 12 = 32
Every value in this data set falls between 0 and 32, so none would be flagged as an outlier by this rule — even though 25 is the largest value, it's still within a normal range for this spread.
Common mistakes to avoid
- Assuming mean and median will always be close — they diverge significantly once a data set is skewed or contains outliers.
- Expecting every data set to have a mode — a set where every value is unique has no mode at all, not a mode of zero.
- Judging spread from range alone — a single extreme value can make the range misleading about how the bulk of the data actually behaves.
- Assuming Q1/Q3 will exactly match between different tools — quartile calculation has more than one accepted convention, so small cross-tool differences are normal.
Related calculators
- Average Calculator — explore geometric, harmonic, and other specialized averages beyond the arithmetic mean.
- Standard Deviation Calculator — measure spread with a metric that uses every data point, not just the extremes.
- Statistics Calculator — get a broader statistical summary including variance and more.
- Z-Score Calculator — see how many standard deviations a value sits from the mean.