A math teacher obtained the following scores from a class of 45 students. Which of the following is the best way to display the frequency of each day of the week?
Test score
50-59
60-69
70-79
80-89
90-99
Number of students
10
4
9
20
2
A.
Scatterplot
B.
Pie graph
C.
Line graph
D.
Histogram
The correct answer and Explanation is :
The best way to display the frequency of each test score range for the class of 45 students is D. Histogram.
Explanation:
A histogram is a type of bar graph that represents the distribution of numerical data by showing the frequency of data points within specified ranges (bins). In this case, the test scores are grouped into ranges: 50-59, 60-69, 70-79, 80-89, and 90-99. Each range corresponds to a bar in the histogram, with the height of each bar indicating the number of students who scored within that range.
Here’s why a histogram is the most appropriate choice for this data:
- Continuous Data Representation: Test scores are continuous data, meaning they can take on any value within a range. A histogram effectively captures the continuous nature of this data by grouping scores into intervals, allowing for a clear visual representation of how many students fall into each score range.
- Easily Interpretable: The heights of the bars in a histogram allow for immediate visual interpretation of the data. For instance, it’s easy to see that the range of 80-89 had the highest frequency with 20 students, while the range of 90-99 had the lowest with just 2 students. This quick visual analysis aids in understanding performance trends within the class.
- Comparison of Frequencies: Histograms facilitate comparison across different intervals. You can quickly compare the number of students who scored in the lower ranges versus the higher ranges, providing insight into the overall performance of the class.
- Simplicity: Creating a histogram is straightforward and doesn’t require complex calculations. You simply need to tally the number of students in each score range and plot it, making it accessible for both teachers and students.
In contrast, other options like scatterplots, pie graphs, or line graphs are not suitable for this type of categorical frequency data. Scatterplots are used for two-dimensional data, pie graphs are better for showing parts of a whole, and line graphs are used for trends over time. Therefore, a histogram is the most effective way to display the frequency of test scores in this scenario.