from. Remembering that some of the funds are riskier than others, Angie is quick to realize that in some years she may not make $15$ percent or more. She may add $25$ percent or higher to her total amount of pension, or she may lose $5$ percent of her pension. An average value doesn$$t guarantee that she will make exactly $15$ percent a year. An average reflects how well she will do when all of the good years $($gains$)$ and bad years $($losses$)$ are combined.

Angie has $20$ years to work before she retires. While this gives her some time to increase her wealth, she is concerned that a few bad years could significantly lower the amount of money that she will retire with. To find the funds that have high gains or high losses, she turns her attention to the study of the range and standard deviation.

QUESTION.

Calculate the range and standard deviation associated with each of the funds and market indicators with an average of $15$ percent or greater return on investment.

PART $4$

For all of the funds that she is interested in$,$ Angie has noticed that the spread of the data differs dramatically. One of the ranges is almost $60$ points! She has also noticed that the riskier the fund, the greater the range of values.

Since the ranges may have been caused by an isolated year that was particularly good or particularly bad, Angie turns her attention to the standard deviations, which also increase as the riskiness of the fund increases.