Online Python classes in Kaiserslautern

days, frost, temp_sum = {}, {}, {}
with open("kaiserslautern_days.txt", encoding="latin-1") as src:
    src.readline()                         # the header row
    for row in src:
        parts = row.split(";")
        year = int(parts[1].strip()[:4])
        t_mean, t_min = float(parts[13]), float(parts[16])
        if t_mean == -999 or t_min == -999:
            continue
        days[year] = days.get(year, 0) + 1
        temp_sum[year] = temp_sum.get(year, 0) + t_mean
        frost[year] = frost.get(year, 0) + (t_min < 0)

full = [y for y in days if days[y] >= 365]
x = [temp_sum[y] / days[y] for y in full]       # mean temperature of the year
y = [frost[yr] for yr in full]                  # days with a minimum below 0 C
print("Complete years:", len(full))
print("Frost days, fewest and most:", min(y), max(y))

The range alone is striking: one complete year in the record has only 34 frost days, 1974, and another has 124, 1955. Version 2 calculates the correlation from scratch, with no library, so every step of the formula is visible: subtract each list's mean, multiply the differences pair by pair, add them up, and divide by the spread of each list.

def mean(v):
    return sum(v) / len(v)

def correlation(a, b):
    ma, mb = mean(a), mean(b)
    top = sum((p - ma) * (q - mb) for p, q in zip(a, b))
    spread_a = sum((p - ma) ** 2 for p in a) ** 0.5
    spread_b = sum((q - mb) ** 2 for q in b) ** 0.5
    return top / (spread_a * spread_b)

print("r between mean temperature and frost days:", round(correlation(x, y), 2))
first = [v for yr, v in zip(full, y) if yr <= 1930]
last = [v for yr, v in zip(full, y) if yr >= 1996]
print("Average frost days 1901 to 1930:", round(mean(first)), " 1996 to 2025:", round(mean(last)))

Figures computed by us from the DWD's daily record for station 02486 (Kaiserslautern), using the daily mean and the daily minimum; file fetched 3 November 2026; licence CC BY 4.0, credit Deutscher Wetterdienst. The rules for a frost day and a complete year are ours.

An r of -0.73 is a strong negative link: in warmer years there are clearly fewer frost days, though not perfectly so. To see that the number is not luck, our learners shuffle the frost counts so that each year gets another year's count, and compute r again: with the order broken it drops to about -0.1. What r cannot do is explain why. It says the two lists move together, not that one causes the other; here the cause is obvious, but for many pairs of numbers it is not, and a high r has fooled many people.

Two more cautions, both from reading the metadata. The station has stood in 15 different places since records began in 1843, and since 1901 its height above sea level has ranged from about 230 to just over 300 metres, which matters for frost. And only 21 of the last 30 years are complete, so the 71 for 1996 to 2025 rests on fewer years than the 77 for 1901 to 1930. Honest analysis states both.

1. Ages 9 to 12. Measure the height and shoe size of ten people. Plot them as dots. Do the dots slope upwards?
2. Teenagers. Run both versions, then shuffle the frost list with the random module and compute r again. Repeat ten times.
3. Adults. Compute r between the year number itself and frost days. What would a strong value mean, and what would it not mean?
4. Going further. Count summer days, with a maximum of 25 degrees or more, and find their correlation with the mean temperature.