WeatherBug Exercise 1 (Math): Temperature Statistics: Max, Min, Range, Median, Mean

The process of calculating an average is not hard, but it can be tedious. So, in math class, the children are often given a set of made-up numbers that make the process easier. In this exercise, you don't get a break; we're going to use real data from the WeatherBug at P.S. 102 for December 1, 2009.  Here are the hourly temperatures:

Dec 1, 2009

Time Temp
12:00 AM 39.5
01:00 AM 38.6
02:00 AM 37.9
03:00 AM 37.7
04:00 AM 37.4
05:00 AM 37.1
06:00 AM 36.2
07:00 AM 36.2
08:00 AM 39.0
09:00 AM 38.9
10:00 AM 40.3
11:00 AM 41.7
12:00 PM 43.9
01:00 PM 43.9
02:00 PM 45.8
03:00 PM 46.0
04:00 PM 46.1
05:00 PM 44.9
06:00 PM 44.8
07:00 PM 44.7
08:00 PM 44.7
09:00 PM 44.5
10:00 PM 44.3
11:00 PM 44.7

Here are the exercises:

  1. What was the low temperature (minimum)?
  2. What was the high temperature (maximum)?
  3. How much did the temperature change that day (range)?
  4. What was the median temperature?
  5. What was the mean temperature?

Solving question 1 requires that we scan through the list of temperatures to find the smallest value. The values at both 6:00 AM and 7:00 AM are the same and are the smallest. So the low temperature on December 1st was 36.2°F.

Solving questiong 2 is like question 1 but we are looking for the largest temperature. That occurred at 4:00 PM when the temperature got up to 46.1°F.

For question 3, the temperature change for the day is just the difference between the high and the low that we found in questions 1 and 2. It was almost 10°F, just a little less at 9.9°F.

For question 4, it's easiest if we reorder the temperatures from lowest to highest so we can find the value in the middle.

Here's a strategy note: if we had carefully read all five questions before starting, we would have noticed that doing question 3 first, which requires that we sort the temperatures to they are all in order (either highest to lowest or lowest to highest, whichever you prefer) would make solving questions 1 and 2 easier. The moral: read all the questions before you start.

For question 5, there is no shortcut. The mean is defined as the the sum of all the values divided by the count. We have 24 temperature measurements and we're just going to have to add them up. If you are doing this in class, I would recommend rounding the temperatures to the nearest degree before adding. That will give an answer which is close enough for our needs. And if you are doing this exercise as a homework assignment, calculators should be allowed. For an average, I get 41.6°F if I use the exact numbers in the columns. And if I round to the nearest degree, I get 41.7°F. In either case, if I round the end result to the nearest degree, I end up with 42°F as the mean temperature for December 1st.

Here's another tip: in math class we often go crazy with getting the exact answer. That's because for things like 1+1=2, there's only one answer and it is exact. But in the sciences, we are often only interested in an approximate answer. For most purposes, knowing the mean temperature to the nearest degree is enough. The difference between 41.6°F and 41.7°F isn't going to make you change your mind about how you dress for the day!

And here's another dirty little secret. While I am not sure about the WeatherBug temperature sensor, most digital temperature sensors have an accuracy of somewhere between 0.1°F and 0.9°F. So going crazy with keeping all those decimal places just doesn't make sense.