Median Calculator — Median, Quartiles, IQR & Mode
Enter a list of numbers to find the median, quartiles (Q1 and Q3), interquartile range (IQR), mode, and range. The distribution curve shows how the median compares to the mean.
Middle value of 9 sorted numbers
- 1
Count values
n = 9 - 2
Middle position
(9 + 1) ÷ 2 = 5 - 3
Median (middle value)
sorted[5] = 5The value at the middle position of the sorted list.
这个计算器是如何工作的？
Sort the data; the median is the middle value (odd n) or average of the two middle values (even n). Q1 and Q3 are the 25th and 75th percentiles; IQR = Q3 − Q1. Unlike the mean, the median is unaffected by extreme outliers, making it the standard central-tendency measure for skewed distributions such as income or house prices.
公式
How this is calculated
To find the median, the calculator sorts the numbers from smallest to largest. For an odd number of values, the median is the single middle entry at position (n+1)/2. For an even count, the median is the average of the two middle values. The result is robust to outliers in a way the arithmetic mean is not — one very large or small value shifts the mean but leaves the median unchanged as long as it does not cross the middle position.
Quartiles divide the sorted dataset into four equal parts. Q1 (the 25th percentile) is the median of the lower half and Q3 (75th percentile) is the median of the upper half, computed here using linear interpolation (equivalent to QUARTILE.INC in Excel). The interquartile range IQR = Q3 − Q1 measures the spread of the middle 50% of values and is used in box-plot construction and outlier detection (values beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR are commonly flagged).
The mode is the most frequently occurring value (or values, for multimodal data). When all values appear exactly once there is no mode. The distribution curve plots a normal approximation centred at the sample mean with the sample standard deviation, marking the median (and mean if notably different) to show whether the data appears symmetric or skewed.
常见问题
The median is preferred when data is skewed or contains outliers. Household income is a classic example: a few very high earners raise the mean far above what most people earn, but the median reflects the middle person. The median is also the standard central-tendency measure for ordinal data and for calculating typical house prices.
The interquartile range IQR = Q3 − Q1 spans the middle 50% of your data. It is a measure of statistical dispersion that ignores extreme values. A small IQR means values are clustered tightly around the median; a large IQR means the central data are more spread out. In box-plot analysis, points more than 1.5 × IQR beyond Q1 or Q3 are typically considered outliers.
A dataset is bimodal (two modes) or multimodal when more than one value occurs with the highest frequency. This often signals that the data comes from two or more distinct subpopulations. When all values are unique, every value occurs exactly once and there is technically no mode.
也称为
TG we-Calculate Editorial Team. (2026). Median Calculator — Median, Quartiles, IQR & Mode [Online calculator]. TG we-Calculate. https://we-calculate.com/zh/calculator/median-calculator
TG we-Calculate Editorial Team. "Median Calculator — Median, Quartiles, IQR & Mode." TG we-Calculate. 2026. https://we-calculate.com/zh/calculator/median-calculator.
TG we-Calculate Editorial Team, "Median Calculator — Median, Quartiles, IQR & Mode," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/zh/calculator/median-calculator
@misc{wecalculate_median_calculator, title = {Median Calculator — Median, Quartiles, IQR & Mode}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/zh/calculator/median-calculator}}, year = {2026}, note = {TG we-Calculate} }
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