Science Daily: Mars
- Surprising insights about debris flows on Mars March 14, 2024
- Giant volcano discovered on Mars March 13, 2024
Science Daily: Uranus
- New images reveal what Neptune and Uranus really look like January 5, 2024
- Ringing in the holidays with ringed planet Uranus December 19, 2023
Science Daily: Pluto
- How Pluto got its heart April 15, 2024
- Evidence of geothermal activity within icy dwarf planets February 15, 2024
Science Daily: Kuiper Belt
- How Pluto got its heart April 15, 2024
- Evidence of geothermal activity within icy dwarf planets February 15, 2024
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
|
Here are the exercises:
- What was the low temperature (minimum)?
- What was the high temperature (maximum)?
- How much did the temperature change that day (range)?
- What was the median temperature?
- 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.
Written by Roland Roberts
Search
.Archives
- April 2024 (3)
- September 2022 (5)
- April 2022 (1)
- January 2022 (3)
- December 2021 (4)
- September 2021 (3)
- July 2021 (1)
- January 2021 (1)
- November 2020 (2)
- October 2020 (2)
- September 2020 (2)
- August 2020 (5)
- July 2020 (1)
- November 2019 (2)
- September 2019 (1)
- August 2019 (2)
- September 2017 (1)
- August 2017 (1)
- September 2015 (3)
- August 2015 (2)
- June 2015 (5)
- May 2015 (3)
- May 2013 (2)
- January 2013 (1)
- December 2012 (2)
- September 2012 (1)
- June 2012 (1)
- May 2012 (1)
- October 2011 (2)
- September 2011 (2)
- April 2011 (2)
- March 2011 (10)
- January 2011 (8)
- November 2010 (2)
- October 2010 (1)
- September 2010 (3)
- August 2010 (2)
- July 2010 (1)
- June 2010 (1)
- April 2010 (3)
- February 2010 (3)
- January 2010 (3)
- December 2009 (6)
- November 2009 (3)
- October 2009 (7)
- September 2009 (8)
- August 2009 (4)
- July 2009 (1)
- June 2009 (2)
- May 2009 (2)
- April 2009 (7)
- March 2009 (1)
- February 2009 (6)
- January 2009 (4)
- December 2008 (4)
- November 2008 (3)
- October 2008 (11)
- September 2008 (4)
- August 2008 (5)
- July 2008 (5)
- June 2008 (2)
- April 2008 (4)
- March 2008 (18)
- February 2008 (9)
- November 2007 (1)
- October 2007 (3)
- July 2007 (3)
- April 2007 (1)
- March 2007 (6)
- February 2007 (3)
- December 2006 (3)
- October 2006 (4)
- September 2006 (1)
- July 2006 (5)
- May 2006 (10)
- April 2006 (9)