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

question 26

Essay

Without calculating the standard deviation, compare the standard deviation for the following 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
$s = \sqrt { \frac { \sum ( x - \bar { x } ) ^ { 2 } } { n - 1 } }$
Data set
1: 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 Data set 2: 20, 25, 25, 30, 30, 30, 30, 35, 35, 40 Date set $3 : 20,20,20,25,25,35,35,40,40,40$

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Definitions:

Crural Region

Pertains to the leg, specifically the area from the knee to the ankle, encompassing the lower limb's anterior and posterior aspects.

Carpal Region

pertains to the area of the wrist that houses the carpal bones.

Sural Region

The sural region pertains to the calf area at the back of the lower leg, commonly referred to when discussing the sural nerve affecting sensation in that area.

Hypogastric Region

Refers to the lower central region of the abdomen, situated below the umbilical region and between the iliac regions.