Let's call the data list in your notebook weatherData
.
Then you can use Cases
(an alternative is Select
, but Cases
is more natural here) to pull out the data in your list that corresponds to the pattern with a June date (advice--time to start learning about patterns: go here and start with the tutorial links at the bottom; this is also in Mathematica itself in the Documentation Ceneter and it's better to learn it there as all the notebooks are Live-- http://reference.wolfram.com/language/ref/Pattern.html ).
juneWeatherData = Cases[weatherData, {{_, 6, _}, _}];
then you can use the earlier approach to pull out just the temperatures from this:
juneTemperatures=juneWeatherData[[All, 2]];
and then compute the mean using:
Mean[juneTemperatures]
Which, for the data in your notebook gives 10.296