Answer :
The data set that represented by the dot plot given is:
D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
In a dot plot, each data point in a data set is represented by a dot.
To find out the data set that is represented in the dot plot, list out the data points as plotted on the dot plot given.
In the given dot plot that is showing the pulse rates of runners after finishing a marathon, it can be seen that,
There are 1 dot on 145, 5 dots on 165, 6 dots on 175 and 1 dot on 185.
Thus:
- 145 - 1 dot = 145
- 165 - 5 dots = 165, 165, 165, 165, 165
- 175 - 6 dots = 175, 175, 175, 175, 175, 175
- 185 - 1 dot = 185
Therefore, the data set that represented by the dot plot given is:
D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
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The correct data set that would be represented in the dot plot, considering the frequencies of each value, is option B: {145, 150, 150, 152, 153, 160, 163, 165, 170, 170, 178, 179, 185}. The correct answer is B. {145, 150, 150, 152, 153, 160, 163, 165, 170, 170, 178, 179, 185}.
To solve this problem, one must understand how to interpret a dot plot. A dot plot is a type of graph that displays data using dots. Each dot represents one occurrence of a value. The position of each dot on the horizontal axis corresponds to the value it represents.
Here is the step-by-step process to determine the correct data set:
1. Identify the unique values represented on the dot plot and count the number of occurrences for each value. This is done by looking at the number of dots above each value on the horizontal axis.
2. List these values and their corresponding frequencies to recreate the data set. For example, if there are two dots above the value 145, then the value 145 should appear twice in the data set.
3. Compare the recreated data set with the options provided to find the match.
Since the actual dot plot is not provided, we can infer from the options given that the correct data set must include all the unique values and their frequencies as they would appear on the dot plot. Option B lists the values 145, 150, 152, 153, 160, 163, 165, 170, 178, 179, and 185 with varying frequencies, which suggests that this set represents the data as it would appear on the dot plot with multiple occurrences of some values (as indicated by the repeated numbers).
Option A does not have enough values to match the dots on the plot. Option C has the correct number of unique values but does not represent the frequencies correctly. Option D incorrectly represents the frequencies of the values, with too many occurrences of 165 and 175.
