Quartile Calculator — Q1, Q2, Q3, IQR & Outliers
Enter a data set to calculate all four quartiles, the interquartile range (IQR), Tukey outlier fences, and the five-number summary — with a distribution visualization showing Q1, Q2 and Q3.
Q3 − Q1 = 31,5 − 10
- 1
Sort & count values
12Data sorted ascending; quartiles are computed from the ordered list. - 2
Q1 — median of lower half
10 - 3
Q3 — median of upper half
31,5 - 4
IQR = Q3 − Q1
31,5 − 10 = 21,5000
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Sort the data, split at the median: Q1 = median of lower half, Q2 = overall median, Q3 = median of upper half (Tukey hinges). IQR = Q3 − Q1. Outlier fences at Q1 − 1.5×IQR and Q3 + 1.5×IQR. Quartiles are robust to outliers and ideal for describing skewed data. Needs ≥ 4 data points.
Képlet
How this is calculated
Quartiles divide a sorted data set into four equal parts. The calculator sorts your numbers in ascending order, then finds Q2 (the overall median) first. It then splits the data into a lower half and an upper half at the median position. When the count is odd, the median value itself is excluded from both halves (Tukey hinges — the same method used by most textbooks, R, and Excel's QUARTILE.EXC). Q1 is the median of the lower half (the 25th percentile); Q3 is the median of the upper half (the 75th percentile).
The interquartile range IQR = Q3 − Q1 describes the spread of the central 50% of the data, immune to the influence of extreme values. Tukey fences identify potential outliers: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged as a mild outlier (this is the standard box-plot whisker rule).
The bell-curve visualization approximates the data as normally distributed, using the mean as centre and estimating the standard deviation as IQR/1.349 (the normal-distribution relationship). The shaded region represents the IQR. This approximation is illustrative — for skewed or multimodal data, the true distribution may differ substantially from the curve shown.
Gyakran ismételt kérdések
Q2 (the median) is the middle value in a sorted data set, while the mean is the arithmetic average. For symmetric distributions they are close. For skewed data they diverge: the mean is pulled toward extreme values, but the median is not. Q2 is the more informative centre measure for skewed data.
Percentiles divide data into 100 equal parts; quartiles are specific percentiles: Q1 = 25th percentile, Q2 = 50th percentile, Q3 = 75th percentile. The IQR is the range from the 25th to the 75th percentile.
There are at least nine different interpolation methods for computing quartiles, and statistical software uses different defaults (e.g. Excel QUARTILE vs QUARTILE.EXC, R's type 7). This calculator uses Tukey hinges (Tukey's method), which is the most common in textbooks and box plots. Differences are usually small for large samples.
Más néven
TG we-Calculate Editorial Team. (2026). Quartile Calculator — Q1, Q2, Q3, IQR & Outliers [Online calculator]. TG we-Calculate. https://we-calculate.com/hu/calculator/quartile-calculator
TG we-Calculate Editorial Team. "Quartile Calculator — Q1, Q2, Q3, IQR & Outliers." TG we-Calculate. 2026. https://we-calculate.com/hu/calculator/quartile-calculator.
TG we-Calculate Editorial Team, "Quartile Calculator — Q1, Q2, Q3, IQR & Outliers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/hu/calculator/quartile-calculator
@misc{wecalculate_quartile_calculator, title = {Quartile Calculator — Q1, Q2, Q3, IQR & Outliers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/hu/calculator/quartile-calculator}}, year = {2026}, note = {TG we-Calculate} }
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