Question

Use the table that lists the weights (in ounces) and operating times (in minutes) for 10 cellular telephones. $$\begin{array}{|c|c|}\hline \text { Wompor } & \text { Caresesum } \\\\\hline 8.8 & 140 \\\\\hline 7.7 & 80 \\\\\hline 4.8 & 90 \\\\\hline 7.0 & 90 \\\\\hline 7.1 & 90 \\\\\hline 8.4 & 70 \\\\\hline 3.8 & 60 \\\\\hline 3.6 & 260 \\\\\hline 6.7 & 75 \\\\\hline 6.2 & 135 \\\\\hline\end{array}$$ Make a stem-and-leaf plot to order the weights of the phones.

Short answer

The stem-and-leaf plot for the weights of the phones is: \n3|6, 8 \n4|8 \n5| \n6|2, 7 \n7|0, 1, 7 \n8|4, 8. This plot shows the sets of phone weights in an organized manner.

Step-by-step solution

Understand Stem-and-Leaf Plots

A stem-and-leaf plot is a kind of data display that uses actual numbers to create a graphic representation of a set of data. In this exercise, the stem will represent the main part of the number and the leaf will represent the decimal portion.

Identify the Stems

The weights given range from 3.6 to 8.8. Therefore, the stem will be made up of the numbers from 3 to 8. So the stem values will be 3, 4, 5, 6, 7, and 8.

Identify the Leaves

The leaves of a stem-and-leaf plot represent the decimal portions of the values given. In this case, for example, 3.6 will be divided into a stem of 3 and a leaf of 6. Do this for all the values.

Create the Stem-and-Leaf Plot

List down the stems and beside each stem, list down the corresponding leaves in increasing order. It should look like: \n3|6, 8 \n4|8 \n5| \n6|2, 7 \n7|0, 1, 7 \n8|4, 8

Key concepts

Data Representation

When we talk about data representation, we refer to the various methods used to display and organize data in a meaningful way. This is crucial, because data in raw form can be overwhelming and difficult to interpret. By representing data visually or numerically, we uncover patterns, trends, and insights that might otherwise remain hidden.

In the context of our exercise, the data representing the weights of cellular telephones is initially provided in a table format. To enhance understanding, we use a stem-and-leaf plot, which furnishes a clearer picture of the distribution of weight values. A well-constructed stem-and-leaf plot not only presents the data systematically but also preserves the actual data points, unlike a bar or pie chart which might aggregate values into categories.

To further improve this data representation, we ensure that our data points are accurate and sorted correctly. In the stem-and-leaf plot, each 'leaf' corresponds to a single weight measurement, and 'stems' represent groups of values, making it easier to identify clusters and outliers. This is particularly helpful for students or data analysts in quickly determining the range, mode, and potential outliers in a set of data.

Statistical Plots

Now, let's delve into the world of statistical plots. These are visual tools used in statistics to represent data graphically. They help people understand and interpret data by summarizing a large amount of information into simple visual forms, such as bar graphs, histograms, pie charts, and of course, stem-and-leaf plots.

Each type of statistical plot has its own strengths and best-use scenarios. For example, bar graphs are excellent for comparing quantities across different categories, while pie charts show proportions as part of a whole. The stem-and-leaf plot, used in our current exercise, is particularly powerful for displaying the shape of a data distribution and the individual values.

One advantage of a stem-and-leaf plot over some other kinds of plots is that it represents both the quantitative data and its distribution while conserving the data's original values. This can be particularly useful in educational settings where students are learning to identify patterns and ranges within sets of numbers. Students should be encouraged to not just create the plot, but also to interpret it, discussing what the plot reveals about the dataset.

Data Analysis

Moving on to data analysis, this area involves inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.

Our exercise focussed on the creation of a stem-and-leaf plot is actually a step within the broad process of data analysis. Through this plot, we could perform a preliminary analysis that leads to a better understanding of the dataset. For instance, we're able to assess the central tendency (like median) and variability (spread of weights) directly from the plot.

To enhance data analysis skills, students should be encouraged to not only create statistical plots but also to deduce possible meanings from them. Questioning how the distribution of weights might affect the overall functionality and user preference of the cellular phones could deepen their analytical thinking. Such a comprehensive approach promotes critical engagement with the data, fostering strong analytical skills for future complex data challenges.