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Chapter 2: Problem 62

The following data give the number of times each of the 30 randomly selected account holders at a bank used that bank's ATM during a 60 -day period. $$ \begin{array}{llllllllll} 3 & 2 & 3 & 2 & 2 & 5 & 0 & 4 & 1 & 3 \\ 2 & 3 & 3 & 5 & 9 & 0 & 3 & 2 & 2 & 15 \\ 1 & 3 & 2 & 7 & 9 & 3 & 0 & 4 & 2 & 2 \end{array} $$ Create a dotplot for these data and point out any clusters or outliers.

Short Answer

Expert verified
The completed dotplot allows us to visualize the frequency of ATM usage within the 60-day period for the bank account holders. Analyzing the plot, it can be clearly observed where the majority of data clusters, and if there are any outliers.

Step by step solution

01

Gather all data

The first step is to organize the data so that it's easier to work with. List all the data given in the problem.
02

Sort the data

In the second step, sort the data from least to greatest. That means rearranging the numbers so they increase in value. Lower numbers like 0, 1, 2 should be to the left, and higher numbers like 15 should be to the right.
03

Create a scale

Before starting the dotplot, it's necessary to create a scale along a horizontal line to represent the data. This line should start from 0 (or the smallest data value) and end at the largest data value. Each number from the data set should have its own point on the scale.
04

Plotting the dots

After the scale is defined, place a dot above the corresponding number on the horizontal line for each data point in the set.
05

Analyzing the dotplot

After plotting all the numbers, look for any clusters, where dots are grouped closely together, and outliers, which are dots far away from others. Clusters signify a greater concentration of data at certain values whereas outliers signify data points that deviate significantly from other observations.

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Key Concepts

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

Understanding Data Visualization with Dot Plots
Dot plots are a simple yet effective way to visualize small sets of numerical data. They help you see the individual data points and their distribution clearly. Imagine drawing a horizontal line, which acts as a scale that represents the possible values in your data set.
To create a dot plot:
  • Mark the data range on a horizontal line. Begin from the smallest number and end with the largest.
  • For each data entry, place a dot above the corresponding value on the horizontal line.
This technique allows for easy interpretation and analysis, perfect for spotting patterns or irregularities in your data. The nature of dot plots makes it simple to pinpoint areas where data points are densely packed or areas that seem empty.
With dot plots, what might remain hidden in raw numbers is often clearly visible.
Spotting Outliers in Your Data
Outliers are data points that deviate significantly from the rest of your dataset. They appear as separate dots on the dot plot, far from the bulk of other points. Outliers can occur because of variability in the data or may indicate a measurement error. Here鈥檚 how you can identify them:
  • Look for dots that are isolated from the main group of data points.
  • Check if they are significantly higher or lower than the rest of the data.
Identifying outliers is important because they can impact the statistical analysis results. In some cases, though, outliers may provide valuable insights into peculiar trends or rare occurrences. Always consider the context of the data while dealing with outliers.
Identifying Data Clusters
Data clusters are groups of data points that are tightly packed together on a dot plot. These clusters indicate concentrations of data points at particular values, suggesting a pattern or trend. Spotting clusters can provide insight into the underlying characteristics of the data set. Here are some tips to identify clusters:
  • Look for groups of dots that are close together or overlapping.
  • Recognize any patterns or repeated occurrences within the cluster.
Clusters can reveal popular or common occurrences within your data set, pointing to consistency or reliability in observations. They help simplify complex data into understandable visual patterns.
The Role of Statistical Analysis in Interpreting Dot Plots
Statistical analysis plays a crucial role in interpreting information from dot plots. By organizing data visually, dot plots lay the foundation for deeper statistical inquiries. Once you have your data plotted:
  • Determine the central tendency, like the mean or median, to understand the average behavior of your data.
  • Analyze the spread or range of the data to find variability.
  • Look at the shape of the distribution. Does it skew left, right, or is it symmetrical?
These analyses provide a more complete understanding of the data beyond simple visual inspection. They help in distinguishing between normal data variations and unusual patterns that might require further investigation. Thus, dot plots, combined with statistical analysis, form a powerful tool for a comprehensive data assessment.

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Most popular questions from this chapter

The accompanying table lists the offensive points scored per game (PPG) by each of the 16 teams in the American Football Conference (AFC) of the National Football League (NFL) during the 2008 season. $$ \begin{array}{lllr} \hline \text { Team } & \text { PPG } & \text { Team } & \text { PPG } \\ \hline \text { Baltimore } & 24.1 & \text { Kansas City } & 18.2 \\ \text { Buffalo } & 21.0 & \text { Miami } & 21.6 \\ \text { Cincinnati } & 12.8 & \text { New England } & 25.6 \\ \text { Cleveland } & 14.5 & \text { New York Jets } & 25.3 \\ \text { Denver } & 23.1 & \text { Oakland } & 16.4 \\ \text { Houston } & 22.9 & \text { Pittsburgh } & 21.7 \\ \text { Indianapolis } & 23.6 & \text { San Diego } & 27.4 \\ \text { Jacksonville } & 18.9 & \text { Tennessee } & 23.4 \\ \hline \end{array} $$ a. Construct a frequency distribution table. Take \(12.0\) as the lower boundary of the first class and \(3.5\) as the width of each class. b. Prepare the relative frequency and percentage distribution columns for the frequency table of part a.

a data set on monthly expenditures (rounded to the nearest dollar) incurred on fast food by a sample of 500 households has a minimum value of $$\$ 3$$ and a maximum value of $$\$ 147 .$$ Suppose we want to group these data into six classes of equal widths. a. Assuming that we take the lower limit of the first class as $$\$ 1$$ and the upper limit of the sixth class as $$\$ 150$$, write the class limits for all six classes. b. Determine the class boundaries and class widths. c. Find the class midpoints.

What is a stacked dotplot, and how is it used? Explain.

In a USA TODAY survey, registered dietitians with the American Dietetic Association were asked, "What is the major reason people want to lose weight?" The responses were classified as Health (H), Cosmetic (C), and Other (O). Suppose a random sample of 20 dietitians is taken and these dietitians are asked the same question. Their responses are as follows. $$ \begin{array}{llllllllll} \mathrm{H} & \mathrm{H} & \mathrm{C} & \mathrm{H} & \mathrm{O} & \mathrm{C} & \mathrm{C} & \mathrm{H} & \mathrm{C} & \mathrm{O} \\ \mathrm{O} & \mathrm{H} & \mathrm{C} & \mathrm{H} & \mathrm{H} & \mathrm{C} & \mathrm{H} & \mathrm{H} & \mathrm{O} & \mathrm{H} \end{array} $$ a. Prepare a frequency distribution table. b. Compute the relative frequencies and percentages for all categories. c. What percentage of these dietitians gave Health as the major reason for people to lose weight? d. Draw a pie chart for the percentage distribution.

A sample of 80 adults was taken, and these adults were asked about the number of credit cards they possess. The following table gives the frequency distribution of their responses. $$ \begin{array}{lc} \hline \text { Number of Credit Cards } & \text { Number of Adults } \\ \hline 0 \text { to } 3 & 18 \\ 4 \text { to } 7 & 26 \\ 8 \text { to } 11 & 22 \\ 12 \text { to } 15 & 11 \\ 16 \text { to } 19 & 3 \\ \hline \end{array} $$ a. Find the class boundaries and class midpoints. b. Do all classes have the same width? If so, what is this width? c. Prepare the relative frequency and percentage distribution columns. d. What percentage of these adults possess 8 or more credit cards?
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