In Part 1 of this question we are given a list of ‘rates of return’ and asked for the Geometric Mean. The geometric mean can be challenging to understand. I cover it’s definition and calculation here, but more importantly – I explain when it is appropriate to use instead of the regular (arithmetic) mean. A typical exam question is used as an example.
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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.
The Empirical Rule gives us our first look in the course at the Normal distribution (a bell shaped frequency distribution of scores). This is an extremely important concept later in the course (Chapter 8 and beyond), so let’s make sure you get a good understanding of its basic characteristics now.
What if the distribution that we’re being asked about is NOT normally distributed? … Or what if we don’t know what the distribution looks like at all? No worries! Chebyshev’s theorem describes ALL distributions – including the normal distribution.
Here we look at the two rules (Empirical and Chebyshev’s) back-to-back. Why learn the Empirical Rule if Chebyshev’s theorem can also handle the normal distribution (as well as every other shape of distribution)? I answer that question here in detail.
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.
Test your understanding of Chapter 4: Numerical Descriptive Techniques – each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.