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 $= \sqrt { \frac { \sum ( x - \bar { x } ) ^ { 2 } } { n - 1 } }$ .

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

---

Definitions:

Sweater

A knitted garment typically with long sleeves, worn over the upper body.

Explanandum

The phenomenon or event that is being explained in a scientific theory or investigation.

Explanation

Providing information or reasons to make something clear or understandable, often answering "why" or "how" questions.

Office Building

A structure designed primarily for occupancy by one or more organizations for the purpose of conducting business or administrative services.