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Temperature variations

You will learn about: statistics and summing lots of numbers.

If you live in the tropics, in the rainforest, near the equator or on an island, the temperature doesn't change a huge amount throughout the year. But if you live in the subtropics or temperate zones then you probably get big swings in temperatures between winter and summer. We can use the average and standard deviation to say things about the climate of a city.

The average (or mean) temperature tells us how warm or cold a place is, while the temperature standard deviation tells us how much the temperature varies. For a series of temperature observations $T_1, T_2, \dots, T_n$, the average temperature $\overline{T}$ is calculated as $$ \overline{T} = \frac{T_1 + T_2 + \cdots + T_n}{n} = \frac{1}{n} \sum_{i=1}^n T_i $$ which can then be used to calculated the temperature standard deviation $\sigma_T$ using $$ \sigma_T = \sqrt{\frac{(T_1 - \overline{T})^2 + (T_2 - \overline{T})^2 + \cdots + (T_n - \overline{T})^2}{n}} = \sqrt{\frac{1}{n} \sum_{i=1}^n (T_i - \overline{T})^2} $$

Average monthly temperatures for five cities. Saskatoon has warm summers and long cold winters so it has the lowest average temperature out of the five cities and the difference the summer and winter is huge so it also has the largest temperature variations. Baku is warmer than Saskatoon so it has a higher average temperature and the seasons aren't as extreme so it has smaller temperature variations. Khartoum is even warmer than Baku with even smaller variations although it gets cooler in July and August with the arrival of the moist south westerlies. Singapore has a tropical rainforest climate and small temperature variations. San Juan, being in the Southern Hemisphere, gets the opposite seasons.

Input: A list of temperatures in degrees Celsius.

Output: The average temperature, and the temperaure standard deviation.


Input temperatures: [4.4, 4.2, 7.0, 12.9, 18.5, 23.5, 26.4, 26.3, 22.5, 16.6, 11.2, 7.3] Output mean: 15.067 Output standard deviation: 8.021
 Difficulty  Timesink
 Function temperature_statistics(T)

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  • We focused on average monthly temperatures but the difference between the warmest temperature in the middle of the day and the coolest temperature in the middle of the night results in a diurnal temperature variation that's also pretty important.
  • You probably noticed a seasonal lag between the time of year with the most sunlight, the summer solstice around June 21, and the warmest months which are usually 1-2 months afterwards in July and August. This is because it takes time to warm things up, especially water with it's huge heat capacity. Because of this, cities near lots of water have longer seasonal lags.
  • A similar lag happens every day where the warmest part of the day is usually around 3-5pm instead of at solar noon when the sun reaches its highest point. As a result, the warmest part of the day is when the sun is setting and is low enough that the surface has started cooling.
  • Wikipedia has a pretty cool list of cities by average temperature.

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