The Christchurch projectThe jackknife on 69 years of Hurn rain
Leave out one year, recalculate, repeat 69 times, and see which statistics survive the treatment.
The Met Office publishes a monthly record for its station at Hurn, a village that postcodes.io places in the same council area as Christchurch. The file begins in January 1957. The learner adds the 12 monthly rainfall figures of each calendar year to get an annual total, keeping the 69 years from 1957 to 2025 that are complete and not marked provisional. The average year brought 845.2 mm. The wettest was 1960 with 1,252.4 mm and the driest 1973 with 509.1 mm.
Three statistics of annual rainfall at Hurn, each recalculated 69 times with one year left out (our Python run on Met Office data)| Statistic | All 69 years | What the 69 recalculations look like | Jackknife standard error |
|---|
| Mean | 845.2 mm | 69 different values, from 839.2 to 850.1 | 17.25 mm |
| Median | 821.7 mm | Only three values: 818.95, 820.45 and 823.2 | 17.41 mm |
| Wettest year | 1,252.4 mm | 68 identical values and one of 1,217.2 | Not meaningful |
For the mean the jackknife is exact. The textbook formula, standard deviation divided by the square root of 69, gives 17.25 mm, and the leave-one-out spread gives 17.25 mm as well. Every year nudges the mean a little, and the nudges add up to an honest measure of doubt. The median behaves differently. Remove any of the 34 drier years and the median becomes 823.2. Remove any of the 34 wetter ones and it becomes 818.95. The whole calculation hangs on three numbers in the middle of the sorted list, so the answer depends on how far apart those three happen to be.
Standard errors as the record grows by one year at a time| Record ends | Years | Mean: jackknife | Median: jackknife |
|---|
| 2021 | 65 | 17.42 mm | 16.88 mm |
| 2022 | 66 | 17.20 mm | 22.17 mm |
| 2023 | 67 | 17.43 mm | 17.15 mm |
| 2024 | 68 | 17.47 mm | 12.28 mm |
| 2025 | 69 | 17.25 mm | 17.41 mm |
One extra year should hardly change how uncertain a 60-odd-year median is. The mean's column agrees: it stays between 17.20 and 17.47. The median's column jumps from 22.17 to 12.28 and back to 17.41, which tells the learner the method is broken here, not the weather. A repair exists within the same idea. Leave out ten years at a time instead of one, over 20,000 random choices, and the median's standard error settles at 23.37 mm, with 22.74 for five years out and 21.89 for twenty. The wettest-year row is worse still: 68 of the 69 recalculations return the same 1,252.4, so leaving one out reveals almost nothing about an extreme.
Ages 8 to 11
Line up seven number cards, take one away at a time, and record what happens to the middle card and to the total.
Ages 11 to 15
Read the Hurn file in Python, build yearly totals, and print the 69 leave-one-out means.
Ages 15 and up
Code the jackknife as a function that accepts any statistic, then find where it fails and try the delete-ten version.
Source and caveats
Contains Met Office data, published as historic station data under the Open Government Licence. Three monthly rainfall values in our span are marked as estimated in the file. Annual totals and every standard error are our calculations. By our measurement the station's coordinates lie 5.87 km from the postcodes.io point for Christchurch, so this is a record for the area and not for any one street. Nothing here is a forecast or a statement about climate.
