Consider the Following Data Set $\begin{array} { l l l l l l l l l l } 46 & 49 & 50 & 52 & 52 & 53 & 56 & 58 & 63 & 71 \end{array}$

question 144

Multiple Choice

Consider the following data set: $\begin{array} { l l l l l l l l l l } 46 & 49 & 50 & 52 & 52 & 53 & 56 & 58 & 63 & 71 \end{array}$
Note: $\bar { x } = 55$ and $s = 7.4$
Also consider the graph of the data set:

Chebychev's rule says that at least 0.75% of the observations lie within 2 standard deviations to either side of the mean. What percentage of the observations actually lie within 2 standard Deviations to either side of the mean?

• A)90%
• B)58%
• C)68%
• D)80%

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Definitions:

Similarity

The state of being alike or having common features or characteristics.

Deductive Step

A step in reasoning in which one proceeds logically from premises to a definite conclusion, ensuring the conclusion necessarily follows.

Evidence

Information or facts that are used to support a belief, conclusion, or argument.

Inductive Step

A crucial part of mathematical proof in inductive reasoning, where one shows that if a property holds for one case, then it also holds for the next case.