EXAMPLE 14 Calculating Standard Deviation Using a TI-84 Graphing Calculator

Next, we compare the fund from Example 12 (Table 5.8) with a different one—the Cohen & Steers Realty Shares (symbol: CSRSX), a mutual fund that invests in real estate investment trusts. Table 5.10 displays its calendar year total returns (in percentages) for the same 10-year period.

Table 5.21: Table 5.10 CSRSX Percentages of Annual Total Return
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
38.48 14.88 37.13 −19.19 −34.40 32.50 27.14 6.18 15.72 3.09

To calculate the mean and standard deviations for these data, we turn to a TI-84 graphing calculator.

  • Step 1: Press (for EDIT). Enter the 10 percentages into list L1 (be sure to clear out any old data first). Here’s a screen shot after entry of the last data value:

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  • Step 2: Press and enter the command for 1-var Stats.

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  • Step 3: Press to obtain the mean and standard deviation. Press the down arrow to obtain the five-number summary.

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Now we are ready to compare the results for the Cohen & Steers Realty Shares (CSRSX) with the results for PIMCO Total Return A (PTTAX). On the one hand, the mean of the 10 CSRSX numbers is approximately 12.15%, which is more than double the mean from the PTTAX data. However, it comes with a tradeoff—a much higher standard deviation of approximately 24.14%. Scanning the numbers in Table 5.10, we see the dramatic lows and highs that make this fund feel like a rollercoaster ride! Knowing how to interpret these numbers is critical when making investment choices to fit your financial goals and tolerance for risk.