Questions: What two types of graphs are most common when the categories are qualitative data? Describe the construction of each.
Select the two choices below that correctly answer the question above.
A. In a frequency table, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents
B. A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each category.
C. In a pie chart, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents.
D. In a bar graph, the categories are clearly indicated along the horizontal axis. Over each category is a rectangle whose height indicates the frequency or relative frequency of the category N the vertical axis clearly indicate the scale.
E. In a pie chart, the categories are clearly indicated along the horizontal axis. Over each category is a rectangle whose height indicates the frequency or relative frequency of the category Nu the vertical axis clearly indicate the scale.
F. In a bar graph, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents.
Transcript text: What two types of graphs are most common when the categories are qualitative data? Describe the construction of each.
Select the two choices below that correctly answer the question above.
A. In a frequency table, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents
B. A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each category.
C. In a pie chart, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents.
D. In a bar graph, the categories are clearly indicated along the horizontal axis. Over each category is a rectangle whose height indicates the frequency or relative frequency of the category N the vertical axis clearly indicate the scale.
E. In a pie chart, the categories are clearly indicated along the horizontal axis. Over each category is a rectangle whose height indicates the frequency or relative frequency of the category Nu the vertical axis clearly indicate the scale.
F. In a bar graph, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents.
Solution
Solution Steps
To determine the two most common types of graphs for qualitative data, we need to identify the correct descriptions of these graphs. Qualitative data is typically represented using pie charts and bar graphs. A pie chart uses wedges to represent categories, with the size of each wedge proportional to the category's relative frequency. A bar graph uses rectangles to represent categories, with the height of each rectangle indicating the frequency or relative frequency.
Step 1: Identify the Graph Types
The two most common types of graphs for qualitative data are the pie chart and the bar graph.
Step 2: Describe the Pie Chart
A pie chart represents categories as wedges of a circle. The size of each wedge is proportional to the relative frequency of the category it represents. This can be expressed mathematically as:
\[
\text{Wedge Size} = \frac{\text{Frequency of Category}}{\text{Total Frequency}} \times 360^\circ
\]
Step 3: Describe the Bar Graph
A bar graph displays categories along the horizontal axis, with rectangles (bars) above each category. The height of each rectangle indicates the frequency or relative frequency of the category. Mathematically, this can be represented as:
\[
\text{Height of Bar} = \frac{\text{Frequency of Category}}{\text{Total Frequency}} \times \text{Max Height}
\]
Final Answer
The correct answers are C and D. Thus, the answer is:
\[
\boxed{\text{C and D}}
\]