/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 The Connecticut Agricultural Exp... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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

Expert verified
The stem-and-leaf plot will show a distribution of calorie content for light beers. From this, we can make a general analysis such as observing where the most common calorie count falls or which calorie count is the least common. Also, due to the small data sample, individual readings (such as unusually high or low calorie beers) are still easy to pick out.

Step by step solution

01

Organize Data

Firstly organize the data in ascending order, it will make it easier to construct the stem-and-leaf display. The numbers range from the teens to the forties.
02

Create Stems

Then, create the stems for the stem-and-leaf plot. As indicated, these stems should be \(1,2,3,4\) representing calories in tens.
03

Add Leaves

Add the leaves to each stem. Each leaf should represent the units digit of each data point. For instance, if you have a data point of 22 calories, '2' would be the leaf that attaches to stem '2'.
04

Construct the Stem-and-Leaf Display

Combine the stems and leaves to create the stem-and-leaf display. Each data point should be represented by a leaf attached to its corresponding stem.
05

Analyze the Stem-and-Leaf Display

Analyze the plot to get information about the data. For instance, check where the median lies, where the majority of data is concentrated, and look out for any 'outliers' that significantly differ from the rest of the data.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Organization
When it comes to understanding vast amounts of numerical information, organizing the data can make a world of difference. The first step in data organization is usually to sort your data. Just like tidying up a cluttered room can help you find what you need faster, organizing data in ascending or descending order simplifies analysis and interpretation.

For instance, if we take the calorie content of different brands of beer from the exercise, organizing them in ascending order allows us to see the range at a glance—from the lightest beer at only 19 calories per 100 ml to the heaviest at 43 calories. Such organization lays the foundation for creating more advanced visuals like charts and diagrams, which facilitate quicker pattern recognition and highlights key statistics within the dataset.
Descriptive Statistics
Descriptive statistics is the aspect of statistics that deals with summarizing and describing the features of a dataset. A typical descriptive analysis includes looking for measures of central tendency (means, medians, and modes) and measures of variability or spread (such as range, variance, or standard deviation).

When students create a stem-and-leaf display, they are using a form of descriptive statistics. This type of plot is particularly handy for displaying frequency distributions of small datasets, as it shows both the shape of the distribution and the individual values. The plot from our exercise would quickly reveal common calorie counts for light beers and how they are distributed. This visualization allows us to grasp basic statistical properties of the data without sophisticated calculations.
Calorie Content Analysis
Analyzing the calorie content of food and beverages is pivotal for understanding dietary impact and making informed nutritional choices. In our case, the exercise is centered around the calorie content analysis of light beers. To have a thorough analysis, one should look beyond just organizing the data and creating a factual representation like the stem-and-leaf display.

For deeper insights, we must assess the central tendency, which might suggest the 'typical' light beer calorie content. Also, identifying outliers is crucial. For example, in the provided data, there is quite a jump from 35 to 40 calories signifying a light beer that might not be so 'light' after all. This simple analysis can reveal trends, such as finding whether most light beers are clustered around a certain calorie content, helping consumers make better choices.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The article "Determination of Most Representative Subdivision" (Journal of Energy Engineering [1993]: \(43-\) 55) gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on the variable \(x=\) total length of streets within a subdivision are as follows: \(\begin{array}{rrrrrrrr}1280 & 5320 & 4390 & 2100 & 1240 & 3060 & 4770 & 1050 \\\ 360 & 3330 & 3380 & 340 & 1000 & 960 & 1320 & 530 \\ 3350 & 540 & 3870 & 1250 & 2400 & 960 & 1120 & 2120 \\ 450 & 2250 & 2320 & 2400 & 3150 & 5700 & 5220 & 500 \\ 1850 & 2460 & 5850 & 2700 & 2730 & 1670 & 100 & 5770 \\ 3150 & 1890 & 510 & 240 & 396 & 1419 & 2109 & \end{array}\) a. Construct a stem-and-leaf display for these data using the thousands digit as the stem. Comment on the various features of the display. b. Construct a histogram using class boundaries of 0 to 1000,1000 to 2000, and so on. How would you describe the shape of the histogram? c. What proportion of subdivisions has total length less than 2000 ? between 2000 and 4000 ?

People suffering from Alzheimer's disease often have difficulty performing basic activities of daily living (ADLs). In one study ("Functional Status and Clinical Findings in Patients with Alzheimer's Disease," Journal of Gerontology [1992]: 177-182), investigators focused on six such activities: dressing, bathing, transferring, toileting, walking, and eating. Here are data on the number of ADL impairments for each of 240 patients: Number of Number of \(\begin{array}{lrrrrrrr}\text { impairments } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\\ \text { Frequency } & 100 & 43 & 36 & 17 & 24 & 9 & 11\end{array}\) a. Determine the relative frequencies that correspond to the given frequencies. b. What proportion of these patients had at most two impairments? c. Use the result of Part (b) to determine what proportion of patients had more than two impairments. d. What proportion of the patients had at least four impairments?

Each observation in the following data set is the number of housing units (homes or condominiums) sold during November 1992 in a region corresponding to a particular Orange County, California, ZIP code: \(\begin{array}{lllrrrrrrrrr}25 & 18 & 16 & 6 & 26 & 11 & 29 & 7 & 5 & 15 & 12 & 37 \\ 35 & 11 & 16 & 35 & 20 & 27 & 17 & 30 & 10 & 16 & 28 & 13 \\ 26 & 11 & 12 & 8 & 9 & 29 & 0 & 20 & 30 & 12 & 45 & 26 \\ 21 & 30 & 18 & 31 & 0 & 46 & 47 & 14 & 13 & 29 & 11 & 18 \\ 10 & 27 & 5 & 18 & 67 & 21 & 35 & 48 & 42 & 70 & 43 & 0 \\ 30 & 17 & 35 & 40 & 61 & 18 & 17 & 17 & & & & \end{array}\) Construct a stem-and-leaf display, and comment on any interesting features.

Disparities among welfare payments by different states have been the source of much political controversy. The accompanying table reports average payment per person (in dollars) in the Aid to Families with Dependent Children Program for the 1990 fiscal year. Construct a relative frequency distribution for these data using equal interval widths. Draw the histogram corresponding to your frequency distribution. $$ \begin{array}{lc} \text { State } & \text { Average Welfare Payment (\$) } \\ \hline \text { Alaska } & 244.90 \\ \text { California } & 218.31 \\ \text { Arizona } & 93.57 \\ \text { Montana } & 114.95 \end{array} $$

The article "Rinse Out Your Mouth" (Associated Press, March 29,2006 ) summarized results from a survey of 1001 adults on the use of profanity. When asked "How many times do you use swear words in conversations?" \(46 \%\) responded a few or more times per week, \(32 \%\) responded a few times a month or less, and \(21 \%\) responded never. Use the given information to construct a segmented bar chart.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.