Question

Watch that caffeine! The U.S. Food and Drug Adminis tration (USFDA) limits the amount of caffeine in a 12-ounce can of carbonated beverage to 72 milligrams. That translates to a maximum of 48 milligrams of caffeine per 8-ounce serving. Data on the caffeine content of popular soft drinks (in milligrams per 8-ounce serving) are displayed in the stemplot.

Part (a). Why did we split stems?

Part (b). Give an appropriate key for this graph.

Part (c). Describe the shape of the distribution. Are there any outliers?

Short answer

Part (a) As a result, we were able to determine the general shape of the distribution.

Part (b) An appropriate key for this stemplot is $\overline{)1}15$indicating that this soft drink contains 15 mg of caffeine per 8-ounce serving.

Part (c)

Right skewed

No outlier

Step-by-step solution

Part (a) Step 1. Given information. 

Stem	Leaf
1	5 5 6
2	0 3 3 3 4 4
2	5 5 6 6 7 7 7 8 8 8 8 8 9 9
3	1 1 3
3	5 5 5 6 7 7 7 8
4	3 3
4	7 7

Part (a) Step 2. Did we split stem 

Stem	Leaf
1	5 5 6
2	0 3 3 3 4 4
2	5 5 6 6 7 7 7 8 8 8 8 8 9 9
3	1 1 3
3	5 5 5 6 7 7 7 8
4	3 3
4	7 7

If we had not split the stems, all data values would have been placed on only four stems (1, 2, 3, 4), making it difficult to determine the general shape of the distribution.

As a result, we divided the stems in order to determine the general shape of the distribution.

Part (b) Step 1. Give an appropriate ate key for this graph

$\overline{)1}556$is the first line of the given stemplot.

This line corresponds to three data values because there are three values to the right of the vertical line. We only need one data value to create an appropriate key, so we limit the right side to one of the values $\overline{)1}5$

The tens are represented by the value to the left of the vertical line, while the ones are represented by the value to the right of the vertical line. 1 | 5 then represents one ten and five ones, corresponding to the number 15.

$1\times 10+5\times 1=15$

As a result, an appropriate key for this stemplot is $\overline{)1}15$, indicating that this soft drink contains 15 mg of caffeine per 8-ounce serving.

Part (c) Step 1. The shape of the distribution Are there any outliers 

The distribution's shape is skewed to the right because the majority of the data values appear to be near the top of the stemplot (corresponding with small data values), with a tail of more unusual data values near the bottom of the stemplot (corresponding with larger data values).

The absence of a gap in the stemplot indicates that there are no outliers in the stemplot.

As a result:

Right skewed

No outlier