Measures of Central Tendency: Arithmetic Means
A portfolio consists of five equally weighted stocks whose annual returns for the year are listed as follows:
| Stock | Return (%) |
|-------|------------|
| A | 11.5 |
| B | 3.9 |
| C | -7.8 |
| D | 24.6 |
| E | -16.2 |
Which of the following statements about the mean is _most appropriate_?
Incorrect.
Since the list includes all stocks in the portfolio, it cannot be treated as a sample.
Moreover, the number 16% is the sum of all returns and is not the mean.
Incorrect.
Consider that this listing includes all 5 stocks which are in the portfolio, and that the mean return in this case is the sum of returns divided by 5.
Correct.
Since the list includes the returns of all five stocks, it is then the population of stocks in the portfolio.
The population mean ($$\mu$$) is the arithmetic mean of all the $$N$$ observations ($$X$$):
$$\displaystyle \mu = \frac{\sum_{i=1}^{N}X_i}{N}$$
$$\displaystyle = \frac{11.5+3.9+24.6+(-7.8)+(-16.2)}{5} = \frac{16}{5}=3.2(\%)$$
[[calc: data 11.5 enter down down 3.9 enter down down 7.8 sign enter down down 24.6 enter down down 16.2 sign enter stat down down , 11.5 sigplus 3.9 sigplus 7.8 chs sigplus 24.6 sigplus 16.2 chs sigplus x]]
The sample mean return for the portfolio is 16%.
The sample mean return for the portfolio is 2.2%.
The population mean return for the portfolio is 3.2%.
