Back in Chapter 9, the Central Limit Theorem showed us that samples are typically representative of the populations from which their drawn. It follows then that the mean of a randomly selected sample should provide a fair estimate of the corresponding population mean.
Regression is all about making predictions. When you make a prediction, you can expect to make mistakes (errors). The Standard Error of the Estimate measures how big of an error we can typically expect. I go through the calculation and the interpretation and introduce the Sum of Squares Error (SSE) along the way.
Now it's time for the main set of numerical techniques presented in this chapter. I start with the measures of central location: the mean, the median, the mode. Next I cover the measures of variation: the range, the variance, the standard deviation, and the coefficient of variation. I also outline which of these are likely to be focused on in the exam.
In Part 2 of this question we are expected to first calculate several rates of return ourselves before determining the Geometric Mean. After this, we once again compare our result to the regular (arithmetic) mean, but part (d) presents us with a follow-up question that highlights a tricky rule that determines when the arithmetic mean is a BETTER choice - even when working with rates of return.
Check out the crazy Chapter 6 question that students in a previous year were expected to solve - and see the answer too!
Here's another typical estimation question, but now we're also asked to interpret our results. Getting this interpretation right is can be tricky - The wording has to be just right to avoid making a common mistake (which they WILL be looking for on the exam).
When questions are focused on finding an unknown population variance or standard deviation, then the chi-squared statistic is used. This question and solution includes a hypothesis test and an estimation as well as how to read the chi-squared table.
This multiple choice question from Chapter 4 covers one of the more challenging theoretical questions from decision analysis.