Question

The mode of the data \(5,\ 7,\ 9,\ 7,\ 11,\ 13,\ 7,\ 15,\ 17,\ 19\) is:

• A. \(5\)
• B. \(7\)
• C. \(11\)
• D. \(15\)

Hint:

Mode means the value that appears the maximum number of times. Think: \[ \text{Mode} \rightarrow \text{Most Frequent} \]

Answer 1

The Correct Option is B

Concept: Mode is the value that occurs most frequently in a data set. It is one of the important measures of central tendency. A data set may have:
• One mode \(\rightarrow\) Unimodal
• Two modes \(\rightarrow\) Bimodal
• More than two modes \(\rightarrow\) Multimodal To find the mode:
• Count the frequency of each observation
• Identify the observation with the highest frequency

Step 1: Writing the given observations carefully.
The given data is: \[ 5,\ 7,\ 9,\ 7,\ 11,\ 13,\ 7,\ 15,\ 17,\ 19 \]

Step 2: Counting the frequency of each observation.
Let us count how many times each number appears.
• \(5\) appears \(1\) time
• \(7\) appears \(3\) times
• \(9\) appears \(1\) time
• \(11\) appears \(1\) time
• \(13\) appears \(1\) time
• \(15\) appears \(1\) time
• \(17\) appears \(1\) time
• \(19\) appears \(1\) time

Step 3: Identifying the observation with maximum frequency.
From the frequency count: \[ 7 \] appears \(3\) times. All other numbers appear only once. Therefore, the number with the highest frequency is: \[ 7 \] Hence: \[ \text{Mode}=7 \]

Step 4: Checking the options carefully.
Option (1): \[ 5 \] Incorrect. Option (2): \[ 7 \] Correct. Option (3): \[ 11 \] Incorrect. Option (4): \[ 15 \] Incorrect. Final Conclusion: The mode of the given data is: \[ \boxed{7} \] Hence, the correct answer is option (2).