As you are well aware, June was unseasonably cold. The mean temperature for June was 63.3°F, which ties it with June 1982 as the sixth coldest June on record in Boston since records began in 1872. Average temperatures of various sorts are often reported by meteorologists, such as the average high or low for a particular day of the year. A statistical quantity that is often overlooked is the standard deviation. That is, when a record occurs, how statistically unlikely is that event compared with the mean?

Your intuition tells you that the standard deviation for Boston temperatures is probably high, since the weather varies greatly from day to day. In places like Los Angeles, California, or Phoenix, Arizona, however, the temperature is fairly constant on a day-to-day time scale, and so the standard deviation is low. Even from month to month, the standard deviation of temperature may vary. For example, in Boston the standard deviation is higher in January than in July.

So just how unusual were the cold temperatures of the past June? The mean temperature for all Junes from 1872 to 2009 is 67.2 °F with a standard deviation of 2.4 °F. Hence, this year's mean June temperature was between one and two standard deviations from the mean. If we average only the high temperatures for June, then this June was the second coldest June with an average high temperature of 69.2 °F. The average high temperature for June is 75.9 °F with a standard deviation of 3.0 °F, making the average high temperature for June 2009 two standard deviations below the average high for June.

The remainder of the work week looks to be cool with sunshine returning on Friday. The weekend warms up with another chance for thunderstorms Saturday evening.