To determine the best representation method for the data, let's analyze the given scores and the distribution of athletes:
1. We have the score points: 1, 2, 3, 4, 5.
2. The number of athletes corresponding to each score point is: 1, 2, 3, 4, 5.
The total number of athletes can be calculated by summing the number of athletes for each score point:
[tex]\[
1 + 2 + 3 + 4 + 5 = 15
\][/tex]
Now, let's consider the different visualization options:
- Histogram: A histogram is suitable for visualizing the distribution of data points when the data are grouped into ranges (bins) or when we have discrete categories (like individual scores in this case) with an associated frequency.
- Line Plot: A line plot is typically used to show trends or changes over a continuous range, often time. It connects individual data points with lines to display the overall trend.
Given the nature of our data (individual scores with discrete categories and their corresponding frequency), a histogram would be more appropriate for representing this data. Here’s why:
- Histogram, because a small number of scores are reported individually: This statement fits our scenario perfectly. The scores are discrete and the number of different scores is small, making it easy to represent each score as a bar in the histogram, showing the frequency of each score clearly.
In conclusion, the best representation for this data is a Histogram, because a small number of scores are reported individually.
