A Population Consists of These Values $3,5,8,14,17$ Find the Mean $\mu$

question 1

Essay

A population consists of these values: $3,5,8,14,17$ . Find the mean, $\mu$ , and standard deviation, $\sigma$ , of the population. List all samples of size $\mathrm { n } = 2$ that are obtained without replacement. Find the population of all values of $\bar { x }$ by finding the mean of each sample that you listed. Find the mean $\mu _ { x } ^ { - }$ and standard deviation $\sigma _ { x } ^ { - }$ for the population of sample means by using the formulas:
$$\mu _ { x } ^ { - } = \mu \text { and } \sigma _ { x } ^ { - } = \frac { \sigma } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$$

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Definitions:

Assessment

A procedure in which information is gathered systematically in the evaluation of a condition; it serves as the preliminary to a diagnosis. A psychiatric assessment may include interviews with the patient or the patient’s family, medical testing, psychophysiological or psychological testing, and the completion of self-report scales or other report rating scales.

Insanity Defence

A legal defense by an accused person claiming that they should not be held legally responsible for their actions due to episodic or persistent psychiatric diseases at the time of criminal act.

Evolution

The process by which different kinds of living organisms are thought to have developed and diversified from earlier forms during the history of the earth.

Mental Disorder

A condition characterized by disordered thought, mood, or behavior that causes significant distress or impairment in personal functioning.