Suppose a pie chart displays the distribution of survey responses among four categories: $A$, $B$, $C$, and $D$. If the chart shows that category $A$ has $10$ responses, $B$ has $15$, $C$ has $20$, and $D$ has $5$, what is the cardinality of the dataset depicted in the pie chart?

• A. $50$
• B. $40$
• C. $10$
• D. $25$

Answer: (A)

Verified step by step guidance

1. Identify the number of responses in each category from the problem: A = 10, B = 15, C = 20, and D = 5.
2. Understand that the cardinality of the dataset refers to the total number of responses across all categories.
3. To find the total number of responses, sum the counts from all categories using the formula: \(\text{Total} = A + B + C + D\).
4. Substitute the given values into the formula: \(\text{Total} = 10 + 15 + 20 + 5\).
5. Calculate the sum to determine the cardinality of the dataset.