Quartiles And Iqr CalculatorFree online math calculator — instant results, no sign-up

Sort the observations as x₁ ≤ x₂ ≤ … ≤ xₙ. For p ∈ {0.25, 0.50, 0.75}, calculate h = 1 + (n − 1)p, j = floor(h), and f = h − j. If j < n, Q(p) = xⱼ + f(xⱼ₊₁ − xⱼ); if j = n, Q(p) = xₙ. Then Q₁ = Q(0.25), Q₂ = Q(0.50), Q₃ = Q(0.75), and IQR = Q₃ − Q₁.

• nNumber of observations in the dataset.
• xᵢObservation at position i in the sorted dataset, using positions starting at 1.
• pPercentile expressed as a proportion: 0.25, 0.50, or 0.75.
• hInterpolated position of the requested percentile in the sorted dataset.
• jInteger part of h, obtained by rounding h down.
• fFractional part of h, which determines how far to interpolate between adjacent observations.
• Q(p)Interpolated value at percentile proportion p.
• Q₁, Q₂, Q₃First quartile, median, and third quartile, respectively.
• IQRInterquartile range: the third quartile minus the first quartile.

Sort the entered observations in ascending order, retaining repeated values. Use the inclusive linear-interpolation position h = 1 + (n − 1)p for each quartile, interpolating between neighboring observations only when the position is fractional. For 2, 4, 6, 8, 10, n = 5, so the quartile positions are 2, 3, and 4. These give Q₁ = 4, Q₂ = 6, and Q₃ = 8; subtracting gives IQR = 8 − 4 = 4.

These are the calculator's starting values and the results it actually produces for them.

1. 1Enter your observations in Values, separated by commas, or leave the default 2, 4, 6, 8, 10.
2. 2Check that all observations are numerical and use consistent units; keep genuine repeated observations.
3. 3Run the calculation to sort the observations and determine the interpolated quartiles.
4. 4Read the First quartile, Median, and Third quartile rows; the default dataset produces 4, 6, and 8.
5. 5Read the IQR row as Third quartile minus First quartile; for the default dataset, this is 8 − 4 = 4.