Chapter 1.2, Problem 46E

(a)

To determine

To explain:the reason for splitting the stems

Answer to Problem 46E

To get a better picture of the distribution, the stems are split.

Explanation of Solution

Given:

1	556
2	033344
2	55667778888899
3	113
3	55567778
4	33
4	77

The stem has been split to get a better picture of the distribution. It has gives two clear peaks at 2 and 3. Splitting of stem gives the better view or shape to the distribution.

(b)

To determine

To give: an appropriate key for this graph.

Answer to Problem 46E

2|4 means that 24 milligrams of caffeine content in 8-ounce can of carbonated beverage

Explanation of Solution

Key: 2|4 means that 24 milligrams of caffeine content in 8-ounce can of carbonated beverage.

(c)

To determine

To describe:the shape, center, and spread of the distribution and compare the caffeine content

Answer to Problem 46E

Shape:skewed to the right

Center: 28mg of caffeine per 8-ounce serving.

Spread: 15 mg to 47 mg of caffeine per 8-ounce serving.

Outliers: none

Explanation of Solution

Shape: the distribution is skewed to the right, because most of the data values lies near the top of the stemplot.

Center: the center of the distribution can be represented as the median which is the middle (19^th data value) value. The 19^th data value is the stemplot is 2|8, which implies that the center is 28mg of caffeine per 8-ounce serving.

Spread: the smallest value is 15 mg and the largest value is 47 mg. thus, the spread will be from 15 mg to 47 mg of caffeine per 8-ounce serving.

Outliers: there do not appear to be any outliers, because there are no gaps in the stemplot (there are no stems without leaves).