IQR Calculator — Interquartile Range & Five-Number Summary
Enter any data set to instantly compute Q1, the median (Q2), Q3, and the interquartile range. The IQR measures the spread of the middle 50% of your data and is robust against outliers.
Middle 50% spread: Q3 − Q1 = 25 − 10
- 1
Q1 — median of lower half
10For odd-length data the overall median is excluded from both halves (Tukey hinges). - 2
Q2 — median of all values
15.5 - 3
Q3 — median of upper half
25 - 4
IQR = Q3 − Q1
25 − 10 = 15
यह कैलकुलेटर कैसे काम करता है?
IQR = Q3 − Q1, the spread of the middle 50% of your data. Sort the values, split in half (excluding the median for odd n), take the median of each half to get Q1 and Q3. The IQR is resistant to outliers, making it ideal for skewed data. Enter at least 4 numbers for a result.
सूत्र
How this is calculated
To find the IQR, the calculator first sorts the data in ascending order, then splits it into two halves at the overall median position. When the count is odd, the median value itself is excluded from both halves (Tukey hinges, the standard method). Q1 is the median of the lower half and Q3 is the median of the upper half; the IQR is simply their difference: Q3 − Q1.
The IQR is the preferred measure of spread for skewed data or data that may contain outliers, because it looks only at the central 50% of observations, ignoring the extremes entirely. The standard deviation, by contrast, is influenced by every value including outliers. A large IQR indicates that the data are more spread out; a small IQR means the values are tightly clustered around the median.
The bell-curve visualization shows a normal-distribution approximation centred on the arithmetic mean, with the standard deviation estimated from the IQR using the relationship σ ≈ IQR / 1.349 (the normal distribution factor). The shaded region between Q1 and Q3 represents the middle 50% of the distribution under normality. If the data are heavily skewed or non-normal, this approximation is illustrative rather than precise.
अक्सर पूछे जाने वाले प्रश्न
The IQR is the range of the middle 50% of the data (Q3 − Q1) and is completely unaffected by outliers. The standard deviation uses every data point and is sensitive to extreme values. For symmetric, bell-shaped data they convey similar information; for skewed data, IQR is more informative.
This calculator uses Tukey hinges (also used by most statistical textbooks and box-plot tools): the median of the lower half gives Q1, and the median of the upper half gives Q3. For an odd number of values, the overall median is excluded from both halves. At least 4 values are needed so each half has a defined median.
Tukey's fence rule flags any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as a mild outlier (3×IQR for extreme). This IQR calculator does not flag outliers — use the IQR & Outlier Calculator for that purpose.
इस नाम से भी जाना जाता है
TG we-Calculate Editorial Team. (2026). IQR Calculator — Interquartile Range & Five-Number Summary [Online calculator]. TG we-Calculate. https://we-calculate.com/hi/calculator/iqr-calculator
TG we-Calculate Editorial Team. "IQR Calculator — Interquartile Range & Five-Number Summary." TG we-Calculate. 2026. https://we-calculate.com/hi/calculator/iqr-calculator.
TG we-Calculate Editorial Team, "IQR Calculator — Interquartile Range & Five-Number Summary," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/hi/calculator/iqr-calculator
@misc{wecalculate_iqr_calculator, title = {IQR Calculator — Interquartile Range & Five-Number Summary}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/hi/calculator/iqr-calculator}}, year = {2026}, note = {TG we-Calculate} }
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