Example 16 The use of alcohol by college students is of grea

Example 1.6 The use of alcohol by college students is of great concern not only to those in the academic community but also, because of potential health and safety consequences, to society at large. The article Health and Behavioral Consequences of Binge Drinking in College reported on a comprehensive study of heavy drinking on campuses across the United States. A binge episode was defined as five or more drinks in a row for males and four or more for females. The figure below shows a display of 140 values of x = the percentage of undergraduate students who are binge drinkers. (These values were not given in the cited article, but our display agrees with a picture of the data that did appear.) The first leaf on the stem 2 row is 1, which tells us that % of the students at one of the colleges in the sample were binge drinkers. Without the identification of stem digits and leaf digits on the display, we wouldn\'t know whether the stem 2, leaf 1 observation should be read as 21%, 2.1%, or 0.21%. When creating a display by hand, ordering the leaves from smallest to largest on each line can be time-consuming. This ordering usually contributes little if any extra information. Suppose the observations had been listed in alphabetical order by school name, as 16g 33g 64g 37g 31g .. . Then placing these values on the display in this order would result in the stem 1 row having 6 as its first leaf, and the beginning of the stem 3 row would be the following. (Enter the first three leaves for this row.) 3| ?.. The display suggests that a typical or representative value is in the stem 4 row, perhaps in the mid-40% range. The observations are not highly concentrated about this typical value, as would be the case if all values were between 20% and 49%. The display rises to a single peak as we move downward, and then ; there are no gaps in the display. The shape of the display is not perfectly symmetric, but instead appears to stretch out a bit more in the direction of low leaves than in the direction of high leaves. Lastly, there are no observations that are unusually far from the bulk of the data (no outliers), as would be the case if one of the 26% values had instead been 86%. The most surprising feature of this data is that, at most colleges in the sample, at least one-quarter of the students are binge drinkers. The problem of heavy drinking on campuses is much more pervasive than many had suspected.

Solution

1. It is a \"stem and leaf\" display.

2. 21%. [answer]

The stem is 2 (tens digit) and the leaf is 1 (ones digit.)

3.

We have 33, 37, 31 as those with 3 as the tens digit.

Thus, the leaves will be 3, 7, 1. [answer]

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4. Please display the options on this 4th question.