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Chapter 2: Problem 46

The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student. \(\begin{array}{llllllllll}32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61\end{array}\) Create a dotplot for these data.

Short Answer

Expert verified
To solve this exercise, you first organize the data, establish a scale on the graph, add dots for every instance of a value and then review the dotplot. You should see higher stacks of dots at values where text messages are sent more frequently.

Step by step solution

01

Understanding Dotplot

A dotplot is a type of graphical display that includes a numerical scale and dots. Each dot represents one observation in the data. They are made to provide detailed visual overviews of small data sets.
02

Organizing the data

To draw a dotplot, we need to organize the data first. The numbers are already arranged in order from least to greatest. Our scope goes from 32 to 61.
03

Establish the scale

On graph paper, draw a horizontal line and mark it with scale, ranging from 32 to 61.
04

Adding dots

For every value, a dot will be placed above the number on the horizontal axis. For instance, if a number is repeated, then the dots are stacked on top of one another.
05

Check the results

After plotting all the dots, you now have a dotplot. You should see higher stacks of dots at values where text messages are sent more frequently.

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Key Concepts

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

graphical display
A dotplot is a simple yet effective type of graphical display used in statistics. It allows us to visually represent numerical data using dots. Each dot corresponds to a data point from the dataset. This method is ideal for small to medium-sized datasets.

By visually plotting the data in this manner, dotplots offer an easy way to see the distribution and frequency of data at a glance. They help in identifying patterns, clusters, and outliers, making it easier to grasp the underlying structure of the dataset.

  • Dotplots are versatile for presenting small datasets.
  • They clearly show how data points are spread out along a number line.
  • Patterns, such as clusters and gaps in the data, can be easily visualized.
numerical scale
The numerical scale on a dotplot is a crucial feature. It represents the range of values in the data on a horizontal line. For the dataset of text messages between 32 and 61, the scale includes every integer in this range.

Drawing a consistent scale is essential for accurate data representation. Each point along this horizontal axis corresponds to an actual data value. The scale helps in comparing different data points effectively.
  • The scale should encompass all data points.
  • Uniform spacing is key for visual clarity.
  • It facilitates easy identification of frequent or rare data points.


Without a clear numerical scale, interpreting a dotplot becomes challenging, as the viewer would not know the exact value each dot represents.
data visualization
Data visualization through dotplots transforms raw numbers into a form that is easy to analyze and interpret. The role of data visualization is to make complex data more accessible and understandable.

In the context of a dotplot, data visualization allows us to see at a glance the number of text messages sent over time. Instead of simply reading raw data numbers, the visual representation provides immediate insights into the behavior or trends of the dataset.

  • Helps in making quick comparisons between data points.
  • It's efficient for spotting trends and patterns in the data.
  • Reveals anomalies that might be hidden in raw data.

By turning data into a visual story, we can better grasp important statistical information without delving too deep into numbers alone.
statistics
Statistics often utilize graphical displays like dotplots to investigate and interpret data. This specific visualization aids in performing a preliminary analysis of data distributions and checking for patterns.

In statistics, understanding the data distribution is fundamental. A dotplot helps in visually confirming assumptions, such as normal distribution or the presence of skewness, which can affect various statistical analyses.

  • Assists in preliminary data analysis.
  • Helps to confirm or challenge assumptions about data patterns.
  • Identifies key features such as central tendency and variability.

Dotplots serve as a stepping stone to more complex statistical analyses, providing a visual foundation to base further inquiries and tests.

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Most popular questions from this chapter

Why do we need to group data in the form of a frequency table? Explain briefly.

The following data give the times (in minutes) taken by 50 students to complete a statistics examination that was given a maximum time of 75 minutes to finish. $$ \begin{array}{llllllllll} 41 & 28 & 45 & 60 & 53 & 69 & 70 & 50 & 63 & 68 \\ 37 & 44 & 42 & 38 & 74 & 53 & 66 & 65 & 52 & 64 \\ 26 & 45 & 66 & 35 & 43 & 44 & 39 & 55 & 64 & 54 \\ 38 & 52 & 58 & 72 & 67 & 65 & 43 & 65 & 68 & 27 \\ 64 & 49 & 71 & 75 & 45 & 69 & 56 & 73 & 53 & 72 \end{array} $$a. Prepare a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order. b. Prepare a split stem-and-leaf display for the data. Split each stem into two parts. The first part should contains the leaves 0 ,

The following table lists the number of strikeouts per game (K/game) for each of the 30 Major League baseball teams during the 2014 regular season. $$ \begin{array}{lclclc} \hline \text { Team } & \text { K/game } & \text { Team } & \text { K/game } & \text { Team } & \text { K/game } \\ \hline \text { Arizona Diamondbacks } & 7.89 & \text { Houston Astros } & 7.02 & \text { Philadelphia Phillies } & 7.75 \\ \text { Atlanta Braves } & 8.03 & \text { Kansas City Royals } & 7.21 & \text { Pittsburgh Pirates } & 7.58 \\ \text { Baltimore Orioles } & 7.25 & \text { Los Angeles Angels } & 8.28 & \text { San Diego Padres } & 7.93 \\ \text { Boston Red Sox } & 7.49 & \text { Los Angeles Dodgers } & 8.48 & \text { San Francisco Giants } & 7.48 \\ \text { Chicago Cubs } & 8.09 & \text { Miami Marlins } & 7.35 & \text { Seattle Mariners } & 8.13 \\ \text { Chicago White Sox } & 7.11 & \text { Milwaukee Brewers } & 7.69 & \text { St. Louis Cardinals } & 7.54 \\ \text { Cincinnati Reds } & 7.96 & \text { Minnesota Twins } & 6.36 & \text { Tampa Bay Rays } & 8.87 \\ \text { Cleveland Indians } & 8.95 & \text { New York Mets } & 8.04 & \text { Texas Rangers } & 6.85 \\ \text { Colorado Rockies } & 6.63 & \text { New York Yankees } & 8.46 & \text { Toronto Blue Jays } & 7.40 \\ \text { Detroit Tigers } & 7.68 & \text { Oakland Athletics } & 6.68 & \text { Washington Nationals } & 7.95 \\ \hline \end{array} $$ a. Construct a frequency distribution table. Take \(6.30\) as the lower boundary of the first class and \(.55\) as the width of each class. b. Prepare the relative frequency and percentage distribution columns for the frequency distribution table of part a.

Stem-and-leaf displays can be used to compare distributions for two groups using a back-to-back stem-and-leaf display. In such a display, one group is shown on the left side of the stems, and the other group is shown on the right side. When the leaves are ordered, the leaves increase as one moves away from the stems. The following stem-and-leaf display shows the money earned per tournament entered for the top 30 money winners in the \(2008-09\) Professional Bowlers Association men's tour and for the top 21 money winners in the 2008 09 Professional Bowlers Association women's tour. $$ \begin{array}{r|c|l} \text { Women's } & & \text { Men's } \\ \hline 8 & 0 & \\ 8871 & 1 & \\ 65544330 & 2 & 334456899 \\ 840 & 3 & 03344678 \\ 52 & 4 & 011237888 \\ 21 & 5 & 9 \\ & 6 & 9 \\ 5 & 7 & \\ & 8 & 7 \\ & 9 & 5 \end{array} $$ The leaf unit for this display is 100 . In other words, the data used represent the earnings in hundreds of dollars. For example, for the women's tour, the first number is 08 , which is actually 800 . The second number is 11 , which actually is 1100 . a. Do the top money winners, as a group, on one tour (men's or women's) tend to make more money per tournament played than on the other tour? Explain how you can come to this conclusion using the stem-and-leaf display. b. What would be a typical earnings level amount per tournament played for each of the two tours? c. Do the data appear to have similar spreads for the two tours? Explain how you can come to this conclusion using the stemand-leaf display. d. Does either of the tours appears to have any outliers? If so, what are the earnings levels for these players?

The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student. \(\begin{array}{llllllllll}32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61\end{array}\) Prepare a stem-and-leaf display for these data.
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