The Average Sales Claim
A sales dashboard reports a team of five and March sales of $184,000. Four full-time reps each sold $38,000; the fifth rep, working 20 hours a week, sold $32,000. The director writes: "Average sales per rep rose from $35,400 in February to $36,800 in March - a 4% gain - so the team improved." In February all five reps were full-time and total sales were $177,000. The part-time arrangement began March 1 and will run through June. The director's bonus depends on showing improvement in average sales per rep.
1. Is the 4% comparison a fair measure of team improvement? Recompute on a like-for-like basis.
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It is not like-for-like, though the arithmetic is correct: 4 × $38,000 + $32,000 = $184,000; $184,000 ÷ 5 = $36,800; $36,800 ÷ $35,400 ≈ 1.040, i.e. +4%.
The composition changed: February had five full-time reps, March had four full-time plus one half-time. Averaging over five heads in March quietly counts a 20-hour person as a full rep.
Comparable measures:
- Same four full-time reps: $38,000 vs. $35,400 = +7.3%.
- Total sales: $184,000 vs. $177,000 = +4.0%.
- Sales per labour hour: February 200 hours → $885/hr; March 180 hours → $1,022/hr = +15.5%.
All three show improvement; the director's own measure is the least informative and would have been distorted by any shift in hours.
2. The part-time rep looks weak on the per-rep average. What does a per-hour view show, and what does it imply for the June decision?
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Per-hour output:
- Part-time rep: $32,000 ÷ 20 hrs = $1,600 per hour.
- Full-time reps: $38,000 ÷ 40 hrs = $950 per hour.
The rep who drags the per-rep average down is the most productive per hour on the team, by about 68%. Splitting the job into 20 hours may have concentrated the highest-value selling time, or the role may differ from the full-time role - either way, the per-rep average punishes the arrangement for a reason unrelated to output.
Implication for June: judge the arrangement on total sales and cost per hour, not headcount average. If the part-time role is genuinely comparable work, extending or expanding it is the strongest move the data supports.
3. The director's bonus depends on this metric. What single reporting change would make the metric hard to game and easy to compare month to month?
Read the worked answer
Report sales per paid labour hour, alongside headcount and total hours.
Why it works:
- It is invariant to how hours are packaged, so moving someone from 40 to 20 hours neither flatters nor penalises the number.
- It cannot be improved by shrinking the denominator without a real output change - cutting hours cuts total sales too.
- It makes hidden assumptions visible: a reader can see 180 versus 200 hours and immediately understand why per-rep and total sales diverge.
Practical formula: total sales ÷ total paid hours, shown with headcount, total hours, and total sales in the same row. Any of the three taken alone can mislead; together they cannot.