mad

std.stats.mad · Level L2

Median absolute deviation, a robust spread: the median distance from the median. Calls median and abs.

median(|x − median(x)|)

Signature

mad(x: f64[n]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

xf64[n]medianmSubtractdabsadmedianmadmadf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.median(np.abs(x - np.median(x))) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 4% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
95%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.72

Identity

Calls
absmedian
Called by
—
sha256:f206d24870e47046ef2148f30c4e607a25aa1fd8e89216792d7283dcabb66116

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.