variance to mean ratio vs coefficient of dispersion

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 = 0.000064scoefficient of dispersion = 0.000064 / 0.000948 ~= 0.07variance 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.

This topic is being discussed at https://groups.google.com/d/topic/maatkit-discuss/Jgs_CCbN76 4/discussion