To determine the best graphical representation of the data, let's analyze the details given in the question:
1. Total Number of Athletes:
- The number of athletes for each score is provided, and we can sum these to find the total number of athletes.
- Number of athletes for each score: 1 (score 1) + 2 (score 2) + 3 (score 3) + 4 (score 4) + 5 (score 5) = 15 athletes.
2. Scores and Number of Athletes:
- Score (points): 1, 2, 3, 4, 5
- Number of athletes: 1, 2, 3, 4, 5
Based on the total number of athletes and the way the scores are distributed individually, each score is uniquely represented without overlapping or being a part of a range.
Graphical Representation Options:
- Histogram:
- Histograms are used to show the distribution of numerical data where data points fall within a range of values. However, in this case, the scores are discrete and individually listed.
- Line Plot:
- Line plots (sometimes referred to as line graphs) are often used for showing data points that are connected and typically for continuous data over intervals.
Given that the scores are discrete and there are a relatively small number of unique scores reported individually (1, 2, 3, 4, 5) rather than as ranges, a histogram makes more sense for visualizing this data, as it allows us to see the frequency of each distinct score.
Conclusion and Selection:
- Histogram, because a small number of scores are reported individually
- This representation is chosen because it effectively displays the frequency distribution of the discrete scores (1 through 5), where each score corresponds uniquely to a number of athletes.
So, the correct answer to represent this data is:
Histogram, because a small number of scores are reported individually.
