Question

The data in Exercises \(1-3\) represent different ways to classify a group of 100 students in a statistics class. Construct a bar chart and pie chart to describe each set of data. $$\begin{array}{c|c}\text { Final Grade } & \text { Frequency } \\\\\hline \mathrm{A} & 31 \\\\\mathrm{~B} & 36 \\\\\mathrm{C} & 21 \\\\\mathrm{D} & 9 \\\ \mathrm{~F} & 3\end{array}$$

Short answer

Question: Construct a bar chart and a pie chart for the given data, which represents the final grades of 100 students in a statistics class. The data is organized in a table format as follows: Grade A = 31 students, Grade B = 36 students, Grade C = 21 students, Grade D = 9 students, and Grade F = 3 students.

Step-by-step solution

Organize the data

Before creating the charts, it's important to have the data organized appropriately. The given data is already organized in a table format which shows the final grade and its corresponding frequency.

Create the bar chart

To create a bar chart, we would need to represent each grade category (A, B, C, D, and F) on the x-axis and the frequency of each grade on the y-axis. Draw a bar with a height corresponding to the frequency of each grade. To make the chart, follow the steps listed below: 1. Set the x-axis labels as the grade categories (A, B, C, D, F). 2. For the y-axis, the scale should start at 0 (zero), and have an appropriate increment (e.g., 5 or 10) that visually represents the data well. 3. Draw a vertical bar for each grade category which extends to the y-axis value corresponding to the frequency of that grade.

Calculate the percentage of each grade

In order to create a pie chart, we need to determine the percentage of students in each grade category. To do this, divide the frequency of each grade by the total students (100) and multiply by 100. Percentage of A = \(\frac{31}{100} \times 100 = 31\%\) Percentage of B = \(\frac{36}{100} \times 100 = 36\%\) Percentage of C = \(\frac{21}{100} \times 100 = 21\%\) Percentage of D = \(\frac{9}{100} \times 100 = 9\%\) Percentage of F = \(\frac{3}{100} \times 100 = 3\%\)

Create the pie chart

To create the pie chart, represent each percentage calculated in Step 3 as a sector (or "slice") of a circle. The total circle represents 100% of the students, and each sector represents the percentage of students who received each letter grade. To make the pie chart, follow these steps: 1. Create a circle. This circle represents 100% of the students. 2. For each grade category (A, B, C, D, F), draw a sector with an angle corresponding to the percentage of that grade (the angle is calculated by multiplying the percentage by 360°). To make it visually clear, add labels and/or colors to identify each sector's corresponding grade. 3. Make sure that all sectors add up to a complete circle (i.e., a total of 100%). After creating the bar chart and pie chart as described, you will have completed the given exercise. Remember to label the charts appropriately as "Bar Chart of Final Grades" and "Pie Chart of Final Grades" respectively.

Key concepts

Bar Chart

A bar chart is a visual representation of data where individual bars represent categories of data. It's an excellent way to display and compare the frequency or quantity of different groups. In our exercise, which aimed to depict student grades, each grade category (A, B, C, D, and F) formed a unique bar on the chart.

To create a bar chart, follow these simple steps:

• Draw a horizontal or vertical axis, with the categorical data on one axis (grade categories) and the quantifiable data on the other (frequency of grades).
• For each category, draw a bar whose height (or length) is proportional to the frequency of that category. For example, the bar for grade B would be the tallest, as it has the highest frequency.
• Ensure the bars are spaced evenly and are of uniform width for clarity.
• Label the axes appropriately to indicate what each represents.

This process not only helps in understanding the distribution of data but also in easily identifying patterns or differences between categories, such as the most or least common grades in this context.

Pie Chart

A pie chart is another graphical tool used to represent data visually. In this circular graph, each "slice" represents a portion of the whole, making it perfect for showcasing data that adds up to 100%, like the percentages of students in each grade.

To construct a pie chart from the exercise data:

• Start with a circle, which symbolizes the complete dataset, in this case, 100 students.
• Calculate the angle for each slice by multiplying the percentage of each category by 360° (as a full circle is 360°).
• Draw each slice based on its calculated angle. For instance, grade B, representing 36% of the students, would be drawn with an angle of 129.6° (36% of 360°).
• Use different colors or labels to make each slice distinct and easily recognizable.

Pie charts offer a quick way to see data composition and relative proportions at a glance, such as easily identifying which grade absorbs the largest or smallest share of the students.

Statistical Graphs

Statistical graphs are vital tools in data visualization, providing both an at-a-glance understanding and detailed insights into data. The two main types of statistical graphs we explored with the exercise data were bar charts and pie charts. Each serves a unique purpose and offers particular benefits.

Bar charts are favored for their ability to compare different categories side by side, making them highly effective when you want to emphasize differences in quantity, such as comparing student grades by frequency.

Pie charts are excellent when the goal is to show proportions within a whole, letting you visually appreciate how each category contributes to the total, like visualizing what fraction of the class attained each grade.

Both graphs require organized data to provide accurate interpretations and need careful attention to detail when being constructed. Labeling and clarity in representation are crucial, as they directly impact the graph's ability to communicate information effectively.

Such graphs serve not only statistical purposes but also pedagogical ones, as they enable students and researchers to convert raw data into more meaningful visual insights that can enhance analysis and decision-making.