Question

your math teacher allows you to choose the most favorable measure of central tendency of your test scores to determine your grade for the term. on 6 tests you earn scores of 81, 87, 79, 84, 94, and 83. what is your grade to the nearest whole number, and which measure of central tendency should you choose?

Answer 1

i'd say choose the mean, because it gives you the highest score.

Answer 2

So, generally you are choosing Mean, Median or Mode.
For median, you pick the middle value of the list (or if even, the two middle ones and divide by two) so:
79,81,83,84,87,94 your median will be (83+84)/2 = 83.5
For Mode, you pick the one that is repeated the most, in this case, there isnt one repeated so mode is undefined (or null).
Mean, depends on what mean you are doing. Generally you will be doing Arithmetic mean, where you sum all the parts and divide by the number of parts. in this case:
(79+81+83+84+87+94)/6 = 84.66
although, there are other Means, Harmonic, for instance (attached):
6/(1/79+1/81+1/83+1/84+1/87+1/94) = 84.40
There is also the geometric mean... where you take the product of all the parts and then take it to the root of the number of parts:\[\sqrt[n]{a_{1}a_{2}a_{3}...a_{n-1}a_{n}}\] which yields:
(79*81*83*84*87*94)^(1/6) = 87.78

So, I would choose to have a Geometric mean, as it is 3 points higher than the normal mean.