Week 5 — The Price Has a History

A single price is easier to judge when you know what it has been before. This week uses price history to tell ordinary prices from unusual ones.

24 August 2026

Core question#

Can today’s price be judged without knowing yesterday’s price?

Week 3 asked where one “was” price came from. This week asks for the whole price history. A price is not fixed; it moves over time.

Baselines, medians, and volatility#

• A baseline built from one past price can be cherry-picked.
• A median over a longer period is harder to fake, because it uses many prices, not one convenient number.
• Volatility means how much the price moves around. It helps you see whether today’s number is normal or unusual.

A price that has sat at $249 for eleven of the last twelve months and spiked to $299 once is a very different object from a price that has bounced between $220 and $310 all year. The single number “$249” cannot distinguish these; the series can.

Rule of thumb: if a price has spent most of a recent window within about 10% of its median, treat a same-range number as ordinary; treat anything further out, in either direction, as worth asking why. This is a classroom heuristic for judging a single price against a short history, not a statistical guarantee.

Hypothetical vs sourced#

This course does not have access to a real retailer’s historical pricing data, and inventing a chart that looks like one would misrepresent it as evidence. Any price series used for teaching in this course is explicitly labelled hypothetical — a plausible shape used to demonstrate the reasoning, not a claim about what any real product has cost. See Policies for how this course draws that line generally.

The $249 headphones#

Hypothetically: suppose the headphones’ price over the past six months looked like a mostly flat line around $249, with a two-week dip to $219 around a mid-year sale event, and no time spent above $260. That shape looks like this:

Against it, $249 reads as an ordinary day — it is the median — not a deal and not a markup. That is a more useful judgement than anything a single was $329 badge could provide, because the badge names one number and the series names the whole distribution it came from.

Notice what the chart makes visible that the sentence above it does not: the dip is one fortnight out of thirteen. A shopper who happened to look in mid-April saw a genuinely unusual price. A shopper who looked in any other fortnight saw the normal one, whatever the badge next to it said.

Learning outcomes#

By the end of this week, you should be able to:

• represent price as a function of time, P(t), rather than a fixed value
• distinguish a baseline built from a single historical price from a median over a longer window
• explain what volatility tells you that a single number cannot
• identify why an invented price series must be explicitly labelled hypothetical
• apply the rule of thumb above to judge whether a price is typical or an outlier, given a short history

Before class#

If you have access to any price-tracking tool, browser history, or your own memory of checking a price more than once, sketch — even roughly — what a chart of that item’s price over the last few months would look like. If you don’t have real data, that’s fine; note that you don’t, and why treating a guess as evidence would be a mistake.

In class#

Work from the hypothetical six-month series charted above. Pick any single fortnight on it, treat that as “today”, and decide: is that price closer to the median, or is it an outlier? State the rule of thumb you used, not just the answer — then swap fortnights with the pair next to you and check whether your two rules agree.

Then try the harder version. Using only the table view of the same series, answer the same question without looking at the line. Which of the two representations made the outlier easier to find, and why?

What you should leave knowing#

A single price is one point in a price history. To judge it fairly, you need the history, or you need to admit that the history is missing.

Where this goes#

Week 6 asks what happens once the price a person sees can depend on who they are, not just on what day it is.