Question 1016068: Here are the noon temperatures (in degrees Celsius) in a particular Canadian city on Thanksgiving Day for the 10 years from 2000 to 2009: 0, 3, 6, 8, 2, 9, 7, 6, 4, 5. Describe the representative (typical) temperature and the amount of variation to a person who has never had a course in statistics. Give three ways of describing the representative temperature and two ways of describing its variation, explaining the differences and how you figured each.
My problem is that I don't understand what they mean by representative temperature. If I can figure that out I think I may be able to figure out how to gain the variation
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the representative temperature is the average, otherwise called the mean.
you need to calculate the mean.
then you need to calculate the variance.
if you need help with any of those, let me know and i'll go through it with you.
here's an example.
you have 3 temperatures.
they are 2,4,6
the representative temperature is (2 + 4 + 6) / 3 = 12/3 = 4
that's the average.
the variance is calculated as follows:
first you get the sum of squares.
that is each temperature subtracted from the mean and then squared.
in this example, you will get:
2 - 4 = (-2) squared = 4
4 - 4 = 0 squared = 0
6 - 4 = 2 squared = 4
sum of squares if 4 + 0 + 4 = 8
sum of squares divided by number of elements is the variance.
you will get variance = 8/3 = 2 and 2/3 = 2.666.... = 2.6667 rounded to 4 decimal places.
your representative temperature is 4.
your variance is 2.6667
your standard deviation is the square root of the variance.
you were not asked to give this, but you will eventually be asked to provide it.
in this example, the standard deviation is the square root of the variance which is the square root of (8/3) which is equal to 1.6330 rounded to 4 decimal places.
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