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

question 139

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

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Definitions:

Subculture

A cultural group within a larger culture, often having beliefs or interests at variance with those of the larger culture.

Social Norms

The accepted behaviors, rules, or standards of conduct expected in a given society or group.

Norm

Accepted standards or expectations of behavior within a society or group.

Mutual Constitution Model

The idea that cultures and selves each cause the other.