Median Absolute Deviation Calculator

Separate values with commas, spaces or new lines.
Different textbooks and calculators split quartiles differently. Pick the one your course uses.
Tukey used 1.5 x IQR for "outliers" and 3 x IQR for "far out" points.
Median absolute deviation
0.5
Descriptive Statistics Calculator
Count (n)
8
Sum
40
Mean
5
Median
4.5
Mode
4
Minimum
2
Maximum
9
Range
7
Midrange
5.5
Sample variance (s squared)
4.571429
Sample standard deviation (s)
2.13809
Population variance (sigma squared)
4
Population standard deviation (sigma)
2
Standard error of the mean
0.755929
Sum of squared deviations (SS)
32
First quartile (Q1)
4
Second quartile (Q2, the median)
4.5
Third quartile (Q3)
5.5
Interquartile range (IQR)
1.5
Lower outlier fence
1.75
Upper outlier fence
7.75
Requested percentile
4.5
Mean absolute deviation
1.5
Coefficient of variation
42.761799 %
Skewness (G1)
0.818488
Excess kurtosis (G2)
0.940625
Worked out from NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5 Quantitative Techniques and 3 other sources.
1 value(s) fall outside the 1.5 x IQR fences: 9.

How this is worked out

8 steps
  1. Sorted data (n = 8): 2, 4, 4, 4, 5, 5, 7, 9
  2. Mean = 40 / 8 = 5
  3. Median = average of the two middle values = 4.5
  4. Sum of squared deviations SS = 32
  5. Sample variance = SS / (n - 1) = 32 / 7 = 4.57142857, so s = 2.13808994
  6. Population variance = SS / n = 32 / 8 = 4, so sigma = 2
  7. Quartiles (linear method): Q1 = 4, Q2 = 4.5, Q3 = 5.5, IQR = 1.5
  8. Outlier fences = Q1 - 1.5 x IQR = 1.75 and Q3 + 1.5 x IQR = 7.75
Modal valuestable
4
Outlierstable
9
Five-number summarytable
2, 4, 4.5, 5.5, 9
Sorted datatable
2, 4, 4, 4, 5, 5, 7, 9

Results are general information, not financial, tax, legal, medical or engineering advice.