The misleading average in reports

The report says: "the average order is 20 lines". The picking shift was planned on that basis, but in practice most orders turned out to have only 2-7 lines, while a single one had more than a hundred. The average does not lie, but it shows only one thing: a total divided by the number of values. How the data are spread is something the average hides, so it should be read critically.

One large order

The number of lines in 10 orders on one day: 2, 3, 3, 4, 4, 5, 5, 6, 7 and 161. The total is 200 and the average 200 ÷ 10 = 20. The median (the middle of the sorted series) is (4 + 5) ÷ 2 = 4.5.

Both numbers are correct, but they answer different questions. The average gives the day's total workload: 10 × 20 = 200 lines to pick. The median shows what a typical order looks like: nine of the ten have up to 7 lines. When the average is far above the median (here 20 and 4.5), the data are stretched to one side, meaning there are one or two very large values.

A quick check: remove the largest value and recalculate the average. Without 161 the other nine add up to 39, giving 39 ÷ 9 ≈ 4.3. A single value moved the average from 4.3 to 20, almost fivefold. That sensitivity is a warning sign.

The decision depends on this. Seven orders have 1-5 lines, two have 6-20, one has more than 21. The small orders need a separate fast-picking lane, while the 161-line order needs its own picker and a pallet. A single process designed around 20 lines would suit neither.

The average of averages

The second trap is a simple average of group percentages. A report gives stock accuracy for two zones: zone 1 at 98 percent (50 positions), zone 2 at 90 percent (450 positions). The simple average (98 + 90) ÷ 2 = 94 percent looks good. But zone 2 has nine times as many positions. The right calculation is weighted: (50 × 0.98 + 450 × 0.90) ÷ 500 = (49 + 405) ÷ 500 = 90.8 percent.

The gap is almost 3 points, and it hides a problem in precisely the bigger zone. In Excel, use SUMPRODUCT(percentages, counts) / SUM(counts) for a weighted average. The separator (comma or semicolon) depends on your Excel settings. The same mistake turns up with fulfilment rates, error shares and margins: each time, check what base the percentages were calculated from.

The average hides the spread

Two suppliers, both with an average delivery time of 5 days. The first one's five deliveries: 5, 5, 5, 5, 5. The second's: 2, 3, 3, 4, 13, so (2 + 3 + 3 + 4 + 13) ÷ 5 = 5. The median is 3 days, but one shipment took 13.

The average is the same, yet for us they are completely different. The first needs hardly any safety stock (σ = 0), the second needs a lot (σ ≈ 4.5 days). If you set the reorder point by the average alone, the second supplier's item will run out.

What to add to a report

• The average and the median side by side.
• The smallest and largest values.
• The 90th percentile: PERCENTILE.INC(range, 0.9) gives a number that is not exceeded in 90 percent of cases. It is useful when you promise an order fulfilment time.
• The number of observations: an average of two or three orders proves nothing.
• A table by group (1-5, 6-20, 21+ lines), which works as a small histogram.

When the average is fine

The average is useful too: for totals (daily workload, monthly costs), when values are spread evenly (say, count time over a large sample) and when comparing changes over a long period. The trouble is not the average itself but using it as the only number.

Conclusion

An average compresses data, and in compressing something valuable is lost. Add the median, the spread and the number of observations to a report and decisions become more precise. In its management report CountLab shows metrics not only as an average but with their spread, and breaks stock count results down by group.