Why does averaged cost data mislead buyers?

Because an average moves with the mix as well as with prices. Blended cost per thousand board feet, per ton or per unit is total spend divided by total quantity. If the business buys more of a cheap item and less of a dear one, that figure falls even when prices have gone up. If it shifts towards dearer items, the figure rises even when prices have come down. A buyer judged on the average can be rewarded for paying more, or blamed for paying less. The standard remedy is to track prices on a fixed basket beside the average, and to split every change into a price effect and a mix effect.

What the usual answer says

The usual answer is that averages hide outliers and skew, and that looking at the distribution or at item-level detail solves it. That is true as far as it goes. An average can do worse than blur the detail. It can point the wrong way.

An average that went the wrong way

From Quarri's own work with a lumber and millwork manufacturer: blended cost per thousand board feet roughly halved while the same basket of goods rose 6%+ in price. The drop came from a change in product mix.

On the spend report, cost per MBF had fallen. The business was paying more for the same basket of goods.

Why it happens

Statisticians have a name for the general pattern. The Stanford Encyclopedia of Philosophy's entry on Simpson's Paradox, by Jan Sprenger and Naftali Weinberger and revised in June 2026, defines it as "a statistical phenomenon where an association between two variables in a population emerges, disappears or reverses when the population is divided into subpopulations". Its opening example shows a treatment with a 50% success rate overall, the same as the control, that does better than the control among both men and women taken separately.

Purchasing works the same way. The subpopulations are items; the overall figure is the blended average. The authors note that such cases "are unproblematic from the perspective of mathematics and probability theory, but nevertheless strike many people as surprising". That surprise is the risk for anyone reading a single cost-per-unit line.

Doesn't purchase price variance already solve this?

Where it is set up and maintained, largely yes. AccountingTools gives the formula as "(Actual price - Standard price) x Actual quantity = Purchase price variance", item by item, so mix can't distort it. The catch is the standard, which it describes as "the price that engineers believe the company should pay for an item". Two things limit it in lumber. The standards have to be reset whenever market prices move, and a stale standard turns every variance into noise. And the figure owners and boards see is often the blended one, because it is a single number on the spend report. In our view the fixed-basket index is the bridge: one number, like the blended average, but immune to mix.

How to report it

This is standard index-number practice. Choose a basket of the items the business buys most, weighted by a base period's quantities, and price it each month at what was actually paid. That is a fixed-weight (Laspeyres-type) index, and it moves only with prices. For any change in average cost between two periods, compute the price effect on the same base-period quantities, and treat the remainder as mix. Using one set of weights for both keeps the index and the split consistent. Mixing base-period and current-period weights gives two different "price" numbers that won't reconcile.

Compare suppliers on the same items, dimensions and grades, not on average cost per MBF.

Where the data work is

The hard part is making items comparable. Suppliers describe the same product differently: a grade abbreviated three ways, a length in feet on one invoice and inches on another, a treatment named in the description rather than a field. AI helps by matching item descriptions across suppliers so like is compared with like, and by checking units. Purchases recorded in pieces or lineal feet and converted to board feet with the wrong factor move the average for a reason that is neither price nor mix, and a unit check catches that before it reaches the index.

When it doesn't apply

A business buying one uniform product, such as a single grade of pulpwood by the ton, has little mix to distort the average. Averages are still the right figure for budgeting total spend, where the mix is part of the plan. And fixed baskets need refreshing now and then, as the items bought change.

Quarri for finance and strategy teams is built for the people who close the month, explain the margin and answer the board.

Quarri is an AI-native data platform for the timber supply chain. It connects buying, production, sales and inventory for forest management, sawmill, wood products and pulp, paper and packaging operators.