 Solution

The mean temperature of a place must specify both the measured quantity and the averaging interval. For a temperature record $T(t)$ over duration $\tau$, the time mean isEqually spaced observations approximate this integral by their arithmetic mean. Irregular observations require time weighting; an unweighted average of many daytime readings and few night-time readings would be biased. A single afternoon observation cannot represent the daily mean.

Observations should use a calibrated thermometer at a stated, consistent exposure, shielded from direct sunlight and other radiative heating while allowing air exchange. Observation time, instrument changes, relocation and missing records must be considered. Daily means can be combined into monthly and annual means with appropriate duration weights. The common approximation $(T_{\max }+T_{\min })/2$ is a defined daily statistic, not an exact identity with the continuous time average.

A long-term climatological normal additionally fixes a reference period. Modern conventional normals commonly use 30 years; that convention is different from claiming that an isolated year's mean is the permanent climate of a place.^[ref]

Places differ because their energy balances and heat transport differ. Latitude changes the distribution of incoming solar radiation and seasonal day length. Altitude, continental or maritime location, prevailing atmospheric circulation, ocean currents, cloud cover, snow cover and local terrain alter heating and cooling. Water's thermal storage moderates coastal variations, but a small annual range does not by itself determine a particular annual mean. Aspect and urban surfaces can also change local exposure. These factors must be distinguished from an artificial difference caused by comparing unlike instruments or observing schedules.^[ref]