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Performance of stock screeners.Investment companies provide their clients with automated tools—called stock screeners—to help them select a portfolio of stocks to invest in. The American Association of Individual Investors (AAII) provides statistics on stock screeners at its Website, www.aaii.com. The next table lists the annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners. (Note:A negative annualized return reflects a stock portfolio that performed worse than the S&P 500.)

(9.0, -.1, -1.6, 14.6, 16.0, 7.7, 19.9, 9.8, 3.2, 24.8, 17.6, 10.7, 9.1)

a.Compute the mean for the data set. Interpret its value.

b.Compute the median for the data set. Interpret its value.

Step by step solution

01

Computing and Interpreting the Mean

$Mean=\frac{Sumofallvalues}{Numberofvalues}$

$$\begin{gathered} Mean=\frac{9.0+\left(-1\right)+\left(-1.6\right)+14.6+16.0+7.7+19.9+9.8+3.2+24.8+17.6+10.7+9.1}{13} \\ =\frac{140.7}{13} \\ =10.82 \end{gathered}$$

As the mean is 10.82, the average annualized percentage return on investments is 10.82%for a portfolio of 13 stocks that were randomly selected.

02

Calculating and Analyzing the Median

By arranging the data in ascending order we get,

(-1.6, -0.1, 3.2, 7.7, 9.0, 9.1, 9.8, 10.7, 14.6, 16.0, 17.6, 19.9, 24.8)

9.8 lies in the middle of the distribution. Hence, 9.8 is the median.

Half of the annualized percentage return on investment is less than 9.8, and half is more than 9.8.

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