The Stockport projectFinding the real turning points
A naive rule, a missing year, and a threshold that separates signal from wobble.
The learner reads the Stockport row of the ORR's Table 1415a into Python: 28 financial years, one of them, 2003-04, shown as x. The first program skips the missing year and marks a peak wherever a year beats both neighbours, and a trough wherever it is lower than both. It finds four peaks and five troughs. Some are real. Others, like the dip in 2014-15 from 3,505,408 to 3,411,494 journeys, are wobbles of under 3 per cent. And the "peak" in 2002-03 exists only because its neighbour, the missing year, was skipped.
Our Python turning points for Stockport station, ORR Table 1415a, 27 September 2026| Rule | Turning points found | Which years | Comment |
|---|
| Any year higher or lower than both neighbours | 9 | From 1998-99 to 2020-21 | Tiny wobbles count; the gap makes one |
| Zigzag, reversal of at least 2% | 10 | Includes the very start | Still noisy |
| Zigzag, reversal of at least 5% | 3 | 2004-05, 2018-19, 2020-21 | The real shape |
| Zigzag, at least 10%, 20% or 50% | 3 | The same three years | Stable, so trustworthy |
The fix is a zigzag rule, borrowed from people who study charts. The program follows the line and only confirms a turning point once it has moved back by a set percentage from the most extreme value so far. With a threshold of 5 per cent the answer drops to three: a low of 1,608,240 journeys in 2004-05, a high of 4,437,070 in 2018-19, and a collapse to 913,096 in 2020-21, 78.8 per cent below the year before. Raising the threshold to 10, 20 or even 50 per cent leaves the same three, which is strong evidence they are real.
The learner writes the lessons down. A missing value should never be quietly skipped when looking for turns, because it can invent one; the report marks 2003-04 as unknown instead. A threshold turns a fussy answer into a useful one, but it must be tested at several values to show the result does not depend on one lucky choice. Tests include a made-up zigzag series whose turning points are known in advance. The table also holds 18 other stations in the borough, from Cheadle Hulme to Bramhall, for anyone who wants to compare.
Ages 8 to 11
Draw a line graph of daily temperatures and circle the highs and lows that really matter.
Ages 11 to 15
Write the neighbour rule in Python, then see what the missing year does.
Ages 15 and up
Build the zigzag rule, sweep the threshold, and compare several stations.
ORR figures, our turning points
The station estimates come from the Office of Rail and Road's Table 1415a. The turning points, thresholds and percentages are our own calculations.
