Coefficient of variation for ratio and inverted ratio

cdelasablonniere

New member
Joined
Aug 19, 2019
Messages
1
Hello all,

I am in not a math expert, so I hope I can get help here.
Here is what I am trying to understand:

I manage an agile software development team.
Each development cycle, the team delivers points by working a certain amount of hours.

I can calculate 2 ratios, which are "inverted" of each other
  1. Points per hours ratio (DP/HW)
  2. Hours per point ratio (HW/DP)
If I calculate the average, standard deviation ad coefficient of variation for each ratio, I would have expected the CV to be the same for both.

Why isn't it the case?

Thanks you for your help,

Charles

Here is a sample of what I did:

Hours WorkedDelivered PointsPoints per hours ratio (DP/HW)Hours per point ratio (HW/DP)
252.33​
15​
0.059445964​
16.822​
244.25​
22.5​
0.092118731​
10.85555556​
240.25​
22​
0.09157128​
10.92045455​
356​
23.5​
0.066011236​
15.14893617​
190.25​
14.5​
0.076215506​
13.12068966​
337.75​
23​
0.068097705​
14.68478261​
379.5​
25.5​
0.067193676​
14.88235294​
345​
25​
0.072463768​
13.8​
435.5​
46​
0.105625718​
9.467391304​
385.5​
39​
0.101167315​
9.884615385​
337.25​
34.5​
0.102297999​
9.775362319​
251.25​
27.5​
0.109452736​
9.136363636​
300.5​
23.5​
0.078202995​
12.78723404​
258​
15.5​
0.060077519​
16.64516129​
383.8​
28.5​
0.074257426​
13.46666667​
451.3​
28​
0.062042987​
16.11785714​
378.3​
33​
0.087232355​
11.46363636​
341​
25​
0.073313783​
13.64​
332.8​
22​
0.066105769​
15.12727273​
344​
22​
0.063953488​
15.63636364​
361.5​
25​
0.069156293​
14.46​
Average
0.078381155​
13.23060457​
Std Dev
0.015600311​
2.402655689​
CV
19.90%​
18.16%​
 
Basically, it doesn't work because ... it just doesn't!

I see no reason to expect that any particular statistic applied to a variable X would be unchanged if you apply it to 1/X, which is in effect what you are doing. A number and its reciprocal behave quite differently. For example, when you take the reciprocal, very small numbers become very very large numbers, and will have a larger effect on the mean than the original numbers do.

Some statistics are designed to cancel out certain changes; the COV is invariant under scaling. But it is not designed to be invariant under the reciprocal.
 
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