To determine which line plot best represents the pulse rates of the goats given in the data set, we first need to count how many times each pulse rate occurs:
- 75 appears 2 times.
- 76 appears 8 times.
- 77 appears 3 times.
- 78 appears 3 times.
- 79 appears 1 time.
With these counts, we can summarize the frequency of each pulse rate:
- 75: 2 dots
- 76: 8 dots
- 77: 3 dots
- 78: 3 dots
- 79: 1 dot
Now let's match these counts with the presented line plots:
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First line plot: 2 dots over 75, 8 dots over 76, 3 dots over 77, 3 dots over 78, no dot over 79. (Incorrect for 79)
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Second line plot: 2 dots over 75, 7 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79. (Incorrect for 76)
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Third line plot: 1 dot over 75, 8 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79. (Incorrect for 75)
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Fourth line plot: 2 dots over 75, 6 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79. (Incorrect for 76)
From the analysis above, the first line plot representation is mostly accurate but missing a dot for 79. However, since the majority of the values match, the first line plot is the closest representation despite that discrepancy.
Therefore, the best answer from the options provided is the first one: line plot with 2 dots over 75, 8 dots over 76, 3 dots over 77, 3 dots over 78, no dot over 79.