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:

Individualistic Cultures

Cultures that emphasize personal achievements, individual rights, and independence.

Individual Rights

Basic freedoms and protections that belong to each person, safeguarding their liberty and equality within a society.

Autonomy

The right or condition of self-government; freedom from external control or influence; independence.

Motivated By Fear

A motivational approach wherein actions or decisions are driven by the desire to avoid negative outcomes, rather than pursue positive ones.