Question

The Connecticut Agricultural Experiment Station conducted a study of the calorie content of different types of beer. The calorie content (calories per \(100 \mathrm{ml}\) ) for 26 brands of light beer are (from the web site brewery.org): \(\begin{array}{lllllllllllll}29 & 28 & 33 & 31 & 30 & 33 & 30 & 28 & 27 & 41 & 39 & 31 & 29\end{array}\) \(\begin{array}{lllllllllllll}23 & 32 & 31 & 32 & 19 & 40 & 22 & 34 & 31 & 42 & 35 & 29 & 43\end{array}\) Construct a stem-and-leaf display using stems \(1,2,3\), and 4\. Write a sentence or two describing the calorie content of light beers.

Short answer

The stem-and-leaf plot is: \(1| 9, 22, 23\), \(2| 7, 8, 8, 9, 9, 9, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5\), \(3| 9\), and \(4| 0, 1, 2, 3\). Most light beers have a calorie count in the twenties and thirties.

Step-by-step solution

Sort the Data

Before creating a stem-and-leaf plot, the data should be sorted: \(19, 22, 23, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 31, 31, 32, 32, 33, 33, 34, 35, 39, 40, 41, 42, 43\)

Create Stems

Next, the stems that represent the tens place of each number should be determined. The stems are \(1, 2, 3, 4\) to be consistent with the given stems. These stems cover all numbers in the dataset since all numbers range between \(19\) and \(43\).

Attach Leafs

Attach the leafs (the unit place of the numbers) to each respective stem: \(1| 9, 22, 23\), \(2| 7, 8, 8, 9, 9, 9, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5\), \(3| 9\), and \(4| 0, 1, 2, 3\).

Write a Description

The calorie content of light beers mostly ranges in the twenties and thirties with a few outliers having calorie counts in the teens and forties.