Standard deviation and variance
Describe how spread out a list of numbers is around its mean. Both sample and population statistics are shown.
MAKE THE FORMULA CLEAR
Median, quartiles and percentiles
Paste a set of numbers to find its median, quartiles or a chosen percentile using linear interpolation.
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Value at the chosen percentile
30
The answer is a data value at the chosen position, not a rank or score percentage. Linear interpolation can produce a number absent from your list. Different quartile definitions can give different answers. Display uses up to 12 significant digits; your original inputs are kept.
Chosen position (%)50
First quartile Q1 (25%)17.5
Median Q2 (50%)30
Third quartile Q3 (75%)50
Interquartile range IQR32.5
Number of data points4 records
Minimum value10
Maximum value80
Worked steps
- 10, 20, 40, 80
- h = 1 + (4 − 1) × 50 ÷ 100 = 2.5
- Q(50%) ≈ 30
Sort the values and find h=1+(n−1)×p/100. Interpolate between neighboring positions using R’s default type 7. Q1, Q2 and Q3 use 25%, 50% and 75%; IQR=Q3−Q1. Keep repeated values, negatives and zero, in the same unit. Quartiles have multiple definitions. This is not the median-of-halves method. A percentile value is not percentile rank, an exam score or the exact share above a threshold. Interpolation may return a value absent from your data. Missing values and outliers are not silently removed; no unseen population is inferred.
Method and scope
Sort the values and find h=1+(n−1)×p/100. Interpolate between neighboring positions using R’s default type 7. Q1, Q2 and Q3 use 25%, 50% and 75%; IQR=Q3−Q1. Keep repeated values, negatives and zero, in the same unit.
Quartiles have multiple definitions. This is not the median-of-halves method. A percentile value is not percentile rank, an exam score or the exact share above a threshold. Interpolation may return a value absent from your data. Missing values and outliers are not silently removed; no unseen population is inferred.
References:Official R documentation: sample quantiles and type 7 interpolation
What this helps you do
Sort a set of observations conceptually to find its middle and dividing values. The median is the 50% position; Q1 and Q3 are 25% and 75%. This page also supports a custom percentile so you do not need separate calculators.
What to enter
Paste 1–200 numbers measured in the same unit, keeping repeated values. Commas, semicolons, spaces or new lines separate observations. Consecutive commas indicate a missing value that must be corrected. Commas are not thousands separators: enter 1000, not 1,000. The position is 0–100, default 50.
How it is calculated
For n sorted values and position p%, use h=1+(n−1)×p/100. A fractional h is linearly interpolated between the neighboring observations. This is R’s default type 7 definition, not a unique definition shared by all textbooks.
Worked example
Synthetic example: for 10, 20, 40, 80, the 25% position is 1.75. Move 75% of the way from 10 to 20 to get 17.5. The median is 30, Q3 is 50, and IQR is 50−17.5=32.5.
Understanding the answer
The main answer is the data value at your chosen percentile. Q1, median, Q3 and IQR summarize the distribution. IQR is Q3 minus Q1, not a mean or each observation’s gap. Interpolated answers need not appear in the original list.
Scope and limitations
Quartile definitions differ; a textbook that splits the list into halves may give another answer. This page is not percentile rank, the percentage of people you beat, or the exact proportion meeting a threshold. Save the original inputs and position for later use. Use standard deviation for spread or weighted mean for supplied weights. No missing values or outliers are automatically removed, and no unseen population is inferred.