Online Python classes in Siegen

temps = []
with open("siegen_days.txt", encoding="latin-1") as f:
    next(f)
    for line in f:
        c = [x.strip() for x in line.split(";")]
        if "20090101" <= c[1] <= "20171231":
            temps.append(float(c[13]))          # daily mean temperature, C

print("Days 2009 to 2017:", len(temps))

hidden = range(10, len(temps) - 10, 10)      # we hide every tenth day ourselves
carry, line = [], []
for i in hidden:
    real = temps[i]
    carry.append(abs(temps[i - 1] - real))                 # copy yesterday
    line.append(abs((temps[i - 1] + temps[i + 1]) / 2 - real))  # halfway between neighbours
print("Hidden days:", len(carry))
print("Copy yesterday, average error:", round(sum(carry) / len(carry), 2), "C")
print("Halfway line, average error:", round(sum(line) / len(line), 2), "C")

Copying yesterday's value is the simplest possible guess, and it is wrong by 1.74 degrees on average. Taking the point halfway between the day before and the day after does clearly better, 1.13 degrees, because it uses information from both sides of the gap. That halfway point is a straight line drawn between two neighbours, and drawing such lines is called linear interpolation. It is used for everything from weather records to animation frames to the brightness of pixels in a resized photo.

def fill(i, gap):
    before, after = temps[i - 1], temps[i + gap]
    step = (after - before) / (gap + 1)
    return [before + step * (k + 1) for k in range(gap)]

for gap in (1, 3, 7, 14):
    errors = []
    for i in range(20, len(temps) - 20, 20):
        guess = fill(i, gap)
        errors += [abs(g - temps[i + k]) for k, g in enumerate(guess)]
    print(f"{gap:>2}-day gap, average error:", round(sum(errors) / len(errors), 2), "C")

Data: Deutscher Wetterdienst, Climate Data Center, daily values for station 04692 Siegen (Kläranlage), daily mean temperature, CC BY 4.0, downloaded 3 November 2026. The hidden days, the guesses and the errors are our own work.

The longer the gap, the worse the line, because weather has fronts and cold snaps that a straight line simply skips. A one-day gap filled by a line is off by about a degree; a two-week gap by more than two and a half. So the honest rule our learners write down is: fill short gaps, label every filled value as estimated, and leave long gaps empty. The four missing years from 1945 to 1948 stay missing.

One more detail rewards careful reading of the metadata. Until 2007 the daily mean at Siegen was calculated from three readings a day, with the evening reading counted twice; from March 2008 it is the average of at least 21 hourly values. That is why we tested only on 2009 to 2017: mixing two methods in one test would blur the answer.

1. Ages 9 to 12. Write the numbers 2, 4, 6, ?, 10 and fill the gap. Then try 2, 4, 9, ?, 10. Is the halfway guess still sensible?
2. Teenagers. Run both versions, then hide every fifth day instead of every tenth. Do the errors change?
3. Adults. Decide the longest gap you would fill in a work dataset, and write one sentence that a colleague could check.
4. Going further. Use the average of the same calendar day in other years as a third guess and compare it with the line for a 14-day gap.