A Statistician Received Some Data to Analyze $\bar { x } \pm s , \bar { x } \pm 2 s$

question 55

Multiple Choice

A statistician received some data to analyze. The sender of the data suggested that the data was normally distributed. Which of the following methods can be used to determine if the data is, in
Fact, normally distributed? I. Construct a histogram and/or stem-and-leaf display of the data and check the shape.
II. Compute the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$ , and $\bar { x } \pm 3 s$ , and determine the percentage of measurements falling in each. Compare these percentages to $68 \% , 95 \%$ , and $100 \%$ .
III. Calculate a value of $\frac { \mathrm { IQR } } { \mathrm { s } }$ . If this value is approximately $1.3$ , then the data is normal.
IV. Construct a normal probability plot of the data. If the points fall on a straight line, then the data is normal.

• A) I only
• B) IV only
• C) I, II, III, and IV
• D) II only
• E) III only

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Definitions:

Groupthink

A phenomenon in group decision-making processes where the desire for harmony or conformity results in an irrational or dysfunctional outcome.

Direct Pressure

A form of influence where someone attempts to coerce others into doing something or changing their behavior through explicit demands, persuasion, or intimidation.

Team's Illusions

False beliefs or perceptions shared among members of a team regarding their effectiveness, cohesion, or capabilities.

Groupthink

A phenomenon in which the desire for group cohesion leads to poor decision-making or the suppression of dissenting opinions within a group.