# 4. Measures of Center Tendency

## e. calculate and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean, geometric mean, harmonic mean, median, and mode;

## m. compare the use of arithmetic mean and geometric means when analyzing investment returns.

What is the most widely used measure of central tendency?

The average (mean)

What is the difference between a population mean and sample mean? How is it displayed differently in math notation?

The population mean has every member of the population. The sample mean has only a subset of the population. The difference is that the sample is displayed with a bar, like $$\bar{x} = \frac{\sum x_i}{N}$$

What does "deviation from the arithmetic mean" mean?

Deviation from the mean is the numerical distance that a given member of the set is from the mean.

What are two disadvantages to using the mean?

1. It can be affected by extremes. Unusually small or large numbers in the set can pull the mean down or up

2. It can't be determined for an open-ended data set (where `N`

is unknown)

What is the math notation for the geometric mean?

$$G = \sqrt[n]{X_1 X_2 ... X_n}$$

What is the geometric mean usually used for in finance?

The geometric mean is typically used when calculating returns over multiple periods. It is a better measure of compound growth rate of an investment.

How is a weighted mean calculated?

The weighted mean is computed by weighting each observed value according to its importance.

How is the weighted mean used to calculate the return of a portfolio?

Each asset in the portfolio is weighted based on its market value relative to the market value of the portfolio.

What is "expected value"?

Expected value is the weighted average of forward looking data.

What is a Median?

The median is the center value in an ordered set. If a set has 9 values, the median is whatever value is at position 5.

What is a Mode?

Mode is the most common number in a data set.

What is the only measure of central tendency that can be used with Nominal values?

Mode. Nominal values are categorical and qualitative, so one of the categories can be the most frequently used.

What is a harmonic mean?

I have no idea. Never heard of it, no description in AnalystNotes...

##### Source:

- CFA