SigmaCalc

Quartiles & IQR Calculator

Split your data into four equal parts and spot the outliers.

Dataset (comma / space / new-line separated)

Q1: 36.75
Q2 (median): 40.5
Q3: 42.75
IQR: 6
Lower fence: 27.75
Upper fence: 51.75

What you entered

Dataset: 10 values

1
Sort the dataset
10 values= 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
2
Q1 (25th percentile)
lower quarter= 36.75
3
Q2 (median, 50th percentile)
middle value= 40.5
4
Q3 (75th percentile)
upper quarter= 42.75
5
Interquartile range: Q3 − Q1
42.75 − 36.75= 6
6
Outlier fences: Q1/Q3 ± 1.5×IQR
36.75 − 1.5×6, 42.75 + 1.5×6= [27.75, 51.75]

Result

IQR: 6

The interquartile range is 6 — any value outside [27.75, 51.75] is a statistical outlier by the 1.5×IQR rule.

Quartiles and interquartile range

Q1 is the median of the lower half, Q3 the median of the upper half, and the IQR is the distance between them - the range of the middle 50%.

Dataset	Q1	Q2 (median)	Q3	IQR
2, 4, 4, 4, 5, 5, 7, 9	4.00	4.50	5.50	1.50
10, 12, 23, 23, 16, 23, 21, 16	15.00	18.50	23.00	8.00
1, 2, 3, 4, 5	2.00	3.00	4.00	2.00
5, 10, 15, 20, 25, 30	11.25	17.50	23.75	12.50
70, 75, 80, 85, 90, 95, 100	77.50	85.00	92.50	15.00
3, 7, 7, 19, 24, 30, 32, 45	7.00	21.50	30.50	23.50

The IQR is the spread measure that ignores outliers by construction, since it discards the top and bottom quarters entirely. Compare rows one and six: both have eight values, but an IQR of 1.50 against 23.50 tells you how much more scattered the second is, and neither figure is affected by how extreme the largest value happens to be. The usual outlier rule flags anything below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times it, which is exactly what draws the whiskers on a box plot. Note that different software uses slightly different quartile conventions, so Q1 and Q3 may vary by a small amount between tools.

Splitting data into quarters

Q1 is the value below which 25% of the data falls, Q2 is the median (50%), and Q3 marks 75% — the interquartile range (Q3 − Q1) captures the middle 50% of your data, ignoring extreme tails entirely.

The 1.5×IQR outlier rule

Any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged as a statistical outlier — this is the same rule that draws the whiskers on a box plot, and it's far more resistant to extreme values than a simple standard-deviation cutoff.

Frequently asked questions

Home prices in a neighbourhood: $180K, $195K, $210K, $225K, $240K, $260K, $890K. Which are outliers?

Q1 = $195K, Q3 = $260K, IQR = $65K. Upper fence = $260K + 1.5×$65K = $357.5K. The $890K house is above the fence — it's a statistical outlier. This is why median home price is more meaningful than mean in real estate.

How is IQR different from standard deviation?

IQR measures the spread of the middle 50% and ignores extremes entirely. SD uses every value and is pulled by outliers. For skewed data (income, house prices, medical costs), IQR is more robust. For symmetric data, SD gives more information. Use the standard deviation calculator for SD.

What are quartiles used for in box plots?

A box plot uses Q1 (left edge of box), Q2/median (line inside box), Q3 (right edge). The box shows the middle 50%. Whiskers extend to the most extreme non-outlier values. Points beyond 1.5×IQR are plotted individually as outliers.