Question

Find the mode of the following dataset: 4, 2, 2, 3, 5, 4, 2?

• A. 2
• B. 3
• C. 4
• D. 6

Hint:

To quickly find the mode, arrange the numbers in ascending order: \( \{2, 2, 2, 3, 4, 4, 5\} \). This groups identical numbers together, making the most frequent value easily visible.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The mode of a dataset is the value that appears most frequently. A dataset can be unimodal (one mode), bimodal (two modes), multimodal, or have no mode at all.

Step 2: Key Formula or Approach:
To find the mode, we count the frequency of occurrence of each distinct value in the given dataset:
\[ \text{Dataset} = \{4, 2, 2, 3, 5, 4, 2\} \]

Step 3: Detailed Explanation:
Let us compile the frequency table for the given dataset:
- Value 2: Appears \( 3 \) times (in positions 2, 3, and 7).
- Value 3: Appears \( 1 \) time.
- Value 4: Appears \( 2 \) times (in positions 1 and 6).
- Value 5: Appears \( 1 \) time.
Comparing the frequencies:
- Frequency of \( 2 = 3 \)
- Frequency of \( 4 = 2 \)
- Frequency of \( 3 = 1 \)
- Frequency of \( 5 = 1 \)
Since the value 2 has the highest frequency of occurrence (appearing 3 times), it is the mode of this dataset.

Step 4: Final Answer
The mode of the given dataset is 2.