Without Calculating the Standard Deviation, Compare the Standard Deviation for the Following

question 101

Essay

Without calculating the standard deviation, compare the standard deviation for the following three data sets. (Note: All data sets have a mean of 30.) Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula s $= \sqrt { \frac { \sum ( x - \bar { x } ) ^ { 2 } } { n - 1 } }$ .

$\begin{array}{cccccccccc}\text { Set A: } 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\\text { Set B: } 20 & 25 & 25 & 30 & 30 & 30 & 30 & 35 & 35 & 40 \\\text { Set C: } 20 & 20 & 20 & 25 & 25 & 35 & 35 & 40 & 40 & 40\end{array}$

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Definitions:

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A mathematical representation of an individual's preference for uncertain outcomes, using probabilities to calculate the expected satisfaction or utility.

Utility Function

A mathematical representation that shows the relationship between the utility or satisfaction a consumer receives and the consumption of various goods and services.

Risk Neutral

A description of an investor or decision maker who is indifferent to risk, focusing solely on the expected outcome without regard to the variability of returns.