# variance to mean ratio  vs coefficient of dispersion

**URL:** <https://forums.percona.com/t/variance-to-mean-ratio-vs-coefficient-of-dispersion/2392>\
**Category:** Other Tools\
**Created:** [March 10, 2011, 4:45am UTC](https://forums.percona.com/t/variance-to-mean-ratio-vs-coefficient-of-dispersion/2392 "2011-03-10T04:45:21Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![rguinot](https://avatars.discourse-cdn.com/v4/letter/r/a88e4f/32.png) [@rguinot](https://forums.percona.com/u/rguinot)\
**Post date:** [March 10, 2011, 4:45am UTC](https://forums.percona.com/t/variance-to-mean-ratio-vs-coefficient-of-dispersion/2392/1 "2011-03-10T04:45:21Z")

</div>

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.

---

<div class="post-metadata">

**Author:** ![xaprb](https://avatars.discourse-cdn.com/v4/letter/x/49beb7/32.png) [@xaprb](https://forums.percona.com/u/xaprb)\
**Post date:** [March 11, 2011, 9:49pm UTC](https://forums.percona.com/t/variance-to-mean-ratio-vs-coefficient-of-dispersion/2392/2 "2011-03-11T21:49:39Z")

</div>

This topic is being discussed at [https://groups.google.com/d/topic/maatkit-discuss/Jgs\_CCbN76](https://groups.google.com/d/topic/maatkit-discuss/Jgs_CCbN76) 4/discussion