The data table represents the volumes of a generic soda brand.
\begin{tabular}{ccc}
\multicolumn{3}{c}{ Volumes of soda (oz) } \\
\hline 75 & 85 & 70 \\
80 & 70 & 75 \\
65 & 70 & 75 \\
65 & 80 & 70 \\
50 & 85 &
\end{tabular}
Complete parts (a) and (b) below.
a. Which plot represents a dotplot of the data?
A
B.
Volumes of soda (oz)
Volumes of soda (oz)
Answer (2)
Count the frequency of each soda volume: 50 (1), 65 (2), 70 (4), 75 (3), 80 (2), 85 (2).
Compare the frequencies to dotplots A and B.
Identify the dotplot that matches the frequencies.
Select the correct dotplot (A or B).
Explanation
Analyze the problem and data We are given a data table of soda volumes and asked to identify the correct dotplot representation. The data table contains the following volumes of soda (in oz): 75, 85, 70, 80, 70, 75, 65, 70, 75, 65, 80, 70, 50, 85.
Count the frequency of each volume First, we need to count the frequency of each distinct volume in the data table.
List the frequencies Using the provided data, we count the occurrences of each volume:
50: 1
65: 2
70: 4
75: 3
80: 2
85: 2
Compare with dotplots Now, we need to compare these frequencies with the dotplots A and B (which are not displayed here). We look for a dotplot where the number of dots above each volume corresponds to its frequency.
Describe the correct dotplot Without the actual dotplots, we can't definitively choose between A and B. However, we can describe what the correct dotplot should look like:
Above 50, there should be 1 dot.
Above 65, there should be 2 dots.
Above 70, there should be 4 dots.
Above 75, there should be 3 dots.
Above 80, there should be 2 dots.
Above 85, there should be 2 dots.
Conclusion Assuming that dotplot A accurately represents these frequencies, we would choose A. If dotplot B represents these frequencies, we would choose B. Since we do not have access to the image, we cannot provide a definitive answer.
Examples
Dotplots are useful for visualizing the distribution of a single variable. For example, a teacher could use a dotplot to visualize the distribution of test scores in a class. This allows the teacher to quickly see the range of scores, the most common scores, and any outliers. This can help the teacher identify students who may need extra help or who are excelling in the subject.
To identify the correct dotplot, count the frequencies of each soda volume from the data table. Compare these counts to the number of dots displayed in dotplots A and B to find the one that matches. Without the images, I cannot definitively tell you which dotplot is correct; you should look for the one with the proper number of dots for each volume.
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