Sample and population variance

The first instance of  is under the Probability and statistics Math Mission. This exercise practices calculation of variance in both sample and population situations.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the mean and variance of the sample: This problem describes the measurements of a sample of all objects from a population. The student is asked to calculate the mean and the variance of the sample.Vars.png
 * 2) Find the mean and variance of the population: This problem describes the measurements of a population. The student is asked to calculate the mean and variance of the population.Varp.png

Strategies
This exercise is medium to get accuracy badges because the calculation is intensive and the rounding restriction is subtle. Speed badges are medium but can be made easier with the calculator.
 * 1) The means are the same for both types of problems, but the sample variance is different than the population variance.
 * 2) The variance is the square of the standard deviation.
 * 3) For a population, the standard deviation is given by $$ \sigma_x $$, but for a sample it is $$ S_x $$.
 * 4) The TI83/84 calculators can find these standard deviations and then you can square them, but read carefully to be sure you are using the correct one.
 * 5) The problem asks answers to be rounded to the nearest tenth, so even if you have an exact decimal but it is to the hundredths, you need to round it to the tenths spot.
 * 6) The default cursor appears in the calculator app, so to start answering you need to click on the answer box.