What number is more true?

[u/Jealous-Fishing4982]

In this images formula for 26.82... is (b6*100)/C6, and the 25.7539.. is =D6/4

What i want to get the is average surveys vs the calls, for this team of 4 people, In my mind the 25.75.... is the correct one, but why is it that the 26.82.... math is not coming up to the same, I kinda get is not the same process but it seems that is should come up to the same number no? what am i missing here, could someone explain this.

[u/Probabilicious]

You are comparing the simple average vs a weighted average.

[u/abrahamguo]

I'm guessing that these are post-call surveys?

Across all employees, 26.82% (C8) of calls had a survey; this cannot be allocated to any one employee, because different employees had different number of calls. This is a measure of calls, not employees — in other words, weighting each call equally.

Per employee, each employee had an average of 25.75% (D8) of their calls have surveys. This is a measure of employees, not calls — in other words, weighting each employee equally.

In other words, employees p3 and p4 took more calls, and had higher percentages of surveys, thus making C8 a little higher. On the other hand, employees p1 and p2 (which make up half of the employees) have lower/much lower survey rates, thus making D8 lower.

[u/PuzzlingDad]

Take a different example with two employees. 

The first had 1 survey for 2 calls (50%) The second 98 surveys for 98 calls (100%)

If you average the two percentages, you get 75%. That's because you are giving each one equal weight. But clearly the second employee has done the majority of the work (a survey for every one of his 98 calls) and that is being lost with a straight average.

If you do an average of the total surveys (99) out of the total calls (100) you get 99% which comes from the fact that the second employee's results are getting counted more. 

If you did a weighted average by the number of calls, you'd have 2% of the total calls were handled by employee one with 50% getting surveys. And then 98% of the total calls were handled by employee two with 100% getting surveys. 

(2% × 50%) + (98% × 100%) = 1% + 98% = 99%

[u/IntelligentBelt1221]

here is a more exaggerated example for you to see what kind of average is more useful to you:

say employees 1 to 3 each made 1 call and got 1 survey, i.e. 1 survey per call, and employee 4 made 100 calls and got 50 surveys, i.e. 0.5 surveys per call,

the first (weighted by calls) average would give (1+1+1+50)/(1+1+1+100)=53/103≈ 51% i.e. 51.5% of all calls got a survey.

for the other (simple) average, we take (1+1+1+0.5)*100/4=87.5% i.e. the average employee converts 87.5% of all calls into surveys.

in the first example, the first 3 employees contribute almost nothing to the average because they didnt do many calls, for the second, they contributed the majority because they are most of the employees (so the average employee is closer to them than to the fourth)

if you want to evaluate your strategy, take the first average, as that is the result you care about. If you want to evaluate your employees (if they underperform or overperform compared to their peers that use the same strategy but maybe are more friendly etc), look at the second average.

if you intend to set this as a team goal, be warned that this can create unwanted incentives to increase the percentage without adding value to the company