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