Quartile Calculator

Your details

Enter values separated by commas or spaces. Spaces and non-numeric entries are ignored. You can enter negative numbers and decimals.
Inclusive uses linear interpolation and matches Excel and NumPy. Exclusive uses the (n+1)p formula favored by many textbooks and TI graphing calculators. Results differ on small datasets.
Show the lower and upper fences (Q1 - 1.5 IQR and Q3 + 1.5 IQR) and flag any values in your dataset that fall outside them.
Interquartile range (IQR)
7
First quartile (Q1)7
Median (Q2)12
Third quartile (Q3)14
Quartile deviation (QD)3.5
Coefficient of quartile deviation0.3333
Tukey lower fence-3.5
Tukey upper fence24.5
Mean (average)11.2222
Range18
Minimum3
Maximum21
Count of values9
Suspected outliers0
Q1 (25th pct)7
Q2 / Median12
Q3 (75th pct)14
IQR (spread)7

Q1 = 7, median = 12, Q3 = 14, IQR = 7.

  • The quartiles divide your 9 values into four equal groups: 25% fall below Q1 (7), 50% below the median (12), and 75% below Q3 (14).
  • The middle 50% of your data spans 7 to 14, a width of 7 (the IQR). The quartile deviation is 3.5.
  • The mean (11.2222) is below the median, suggesting the data may be skewed left (negative).
  • No values fall outside the Tukey fences (-3.5 to 24.5), so there are no suspected outliers.

Next stepUse Q1, Q2, Q3, the minimum, and the maximum to draw a box-and-whisker plot. Points beyond the Tukey fences are conventionally plotted as individual dots.

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