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[maatkit-discuss] variance to mean ratio vs coefficient of dispersion


Romain GUINOT Mar 11, 2011 2:39 AM
Posted in group: Maatkit Help
Hi,

I have a little statistics question about the variance to mean (V/M)
value reported by mk-query digest.

let's consider this output :

# Attribute    pct   total     min     max     avg     95%  stddev
median V/M
# ============ === ======= ======= ======= ======= ======= =======
======= ====
# Count         12  160000
# Exec time     11    152s       0      1s   948us   972us     8ms
972us 0.07


(i have added the v/m column from the profile output).

From my understanding :


* variance V(X) is the mean of the squared distances to the mean
* std dev is the squared root of the variance
* variance to mean = the ratio of the variance (σ) squared to the mean
(µ) : σ^2/ μ
* coefficient of dispersion = variance to mean : σ / µ

For the sample above, we have :

stddev = 0.008 = sqrt(variance)
variance = 0.008^2 = 64µs = 0.000064s
coefficient of dispersion = 0.000064   / 0.000948 ~= 0.07
variance to mean ratio    = 0.000064^2 / 0.000948 ~= 0.000004


Based on the sample above, i think mk-query-digest reports the
coefficient of dispersion, not the variance to mean.

Am i correct ?

Cheers,
Romain.