Consider the data set: 12, 1, 10, 1, 9, 3, 4, 9, 7, 9. What is the mode of this data?

Introduction / Context:
This question is taken from basic statistics and tests your understanding of the concept of mode. The mode is the value that occurs most frequently in a data set. Unlike the mean and median, which are measures of central tendency based on position or arithmetic combinations, the mode is purely frequency based.

Given Data / Assumptions:

The data set is: 12, 1, 10, 1, 9, 3, 4, 9, 7, 9.
All values are treated as distinct observations in a simple list (no grouping or class intervals).
We assume that we are asked to find the unique mode if it exists, that is, the single most frequent value.

Concept / Approach:
The mode of a data set is defined as the value that appears the greatest number of times. To find it, we count the frequency of each distinct number in the list. The number with the highest frequency is the mode. If two or more numbers are tied for highest frequency, the data set is multimodal, but in this problem one value clearly appears most often.

Step-by-Step Solution:
Step 1: List each distinct value and count frequencies. Values present: 1, 3, 4, 7, 9, 10, 12. Count for 1: appears twice. Count for 3: appears once. Count for 4: appears once. Count for 7: appears once. Count for 9: appears three times. Count for 10: appears once. Count for 12: appears once. Step 2: Identify the highest frequency. The highest frequency is 3, corresponding to the value 9. Therefore, the mode of the data set is 9.

Verification / Alternative Check:
We can quickly verify by re-scanning the original list: 12, 1, 10, 1, 9, 3, 4, 9, 7, 9. Counting again, 9 appears at three positions, 1 at two positions, and all other numbers appear only once. Since 9 clearly has the maximum frequency, the mode is unambiguously 9. No other value matches its frequency.

Why Other Options Are Wrong:
12 appears only once, so it cannot be the mode.
1 appears twice, but this is fewer than the three occurrences of 9.
7 also appears only once and therefore is not the most frequent value.

Common Pitfalls:
Learners sometimes confuse mode with mean or median and try to perform arithmetic operations instead of frequency counting. Another common error is to miscount the occurrences of each value, especially in longer lists. Taking a systematic approach—listing each distinct value and tallying occurrences—helps ensure that the correct mode is identified.

Final Answer:
The mode of the given data set is 9.