Probability and Statistics: Making Sense of Randomness
What probability means, how the bell curve works, what z-scores and confidence intervals actually tell you, and why sample size matters.
A day at 32°C with 40% humidity feels warm but bearable. The same 32°C with 80% humidity feels like walking into a wall of heat. The thermometer reads the same number, but your body tells a completely different story. The difference is the heat index — and understanding it can be a matter of safety.
Relative humidity (RH%) is the percentage of moisture in the air relative to the maximum it can hold at that temperature. Warm air holds more water vapour than cold air, so 50% RH at 35°C contains far more water than 50% RH at 10°C.
This is why RH alone is a poor comfort indicator. A reading of 90% RH at 15°C feels cool and damp. The same 90% RH at 35°C is dangerously oppressive.
The dew point is the temperature at which the air becomes fully saturated and water begins to condense. Unlike RH, the dew point is an absolute measure — it does not change with air temperature. Meteorologists consider it a superior comfort metric:
| Dew point | Comfort level |
|---|---|
| < 10°C (50°F) | Dry and pleasant |
| 10-15°C (50-59°F) | Comfortable |
| 16-18°C (60-65°F) | Slightly humid |
| 19-21°C (66-70°F) | Humid, noticeable |
| 22-24°C (71-75°F) | Oppressive |
| > 24°C (75°F) | Dangerous, tropical extremes |
The heat index combines air temperature and relative humidity into a single “apparent temperature” — what the weather app calls “feels like.” High humidity blocks sweat evaporation, which is the body's primary cooling mechanism. When sweat cannot evaporate, your core temperature rises.
The US National Weather Service calculates heat index using the Rothfusz regression formula — a polynomial with nine terms. It was developed by R.G. Steadman in 1979 and refined by Rothfusz in 1990. The formula is accurate for temperatures above 27°C (80°F) and RH above 40%.
NWS Heat Index Danger Levels:
27-32°C (80-90°F) → Caution: fatigue possible
32-39°C (90-103°F) → Extreme Caution: cramps, exhaustion possible
40-51°C (104-124°F) → Danger: cramps/exhaustion likely, heatstroke possible
> 51°C (> 124°F) → Extreme Danger: heatstroke highly likelyWhile heat index adds perceived heat, wind chill subtracts perceived warmth. Wind accelerates heat loss from exposed skin. The current NWS wind chill formula (revised in 2001) models a human face walking at 1.3 m/s at face height:
At −10°C with a 30 km/h wind, the wind chill is approximately −20°C. Frostbite can develop in 30 minutes under these conditions. Below −27°C wind chill, exposed skin can freeze in under 10 minutes.
A British Thermal Unit (BTU) is the energy needed to raise one pound of water by 1°F. Air conditioners and furnaces are rated in BTUs per hour. Choosing the right capacity depends on several factors:
An AC unit that is too powerful for the room cools the air quickly but shuts off before removing humidity. The result: a cold, clammy room that cycles on and off constantly, wasting energy and wearing out the compressor. Proper sizing matters more than raw power.
Dew point, heat index, wind chill, and BTU ratings are all attempts to bridge the gap between what instruments measure and what humans experience. A thermometer reads air temperature, but comfort depends on moisture, wind, radiation, and the body's ability to regulate heat.
The weather is not what the thermometer says. It is what your body feels — and understanding the science behind that gap is the first step to staying safe in extreme conditions.
What probability means, how the bell curve works, what z-scores and confidence intervals actually tell you, and why sample size matters.
Area and volume formulas for every common shape, the Pythagorean theorem, Law of Sines and Cosines, and slope of a line.
How fractions work, why prime factorisation matters, the GCF and LCM connection, ratios, proportions, and percentages as fractions of 100.