For the data 6, 3, 8, 4, 3, 11, 7, 4, 5 and 4, find the sum of the mode, the median and the mean.

Introduction / Context:
This question brings together three basic measures of central tendency: mean, median and mode. You must compute each of them for the same data set and then find their sum.

Given Data / Assumptions:
- The data points are 6, 3, 8, 4, 3, 11, 7, 4, 5 and 4.
- We must calculate the mode (most frequent value), median (middle value when sorted) and mean (arithmetic average).
- Finally, we must add these three measures together.

Concept / Approach:
To find the mode, we count how many times each value appears. To find the median, we sort the data and look at the middle value or the average of the two middle values. For the mean, we divide the total sum by the number of observations. Then we simply add the three results.

Step-by-Step Solution:
Step 1: Sort the data in ascending order: 3, 3, 4, 4, 4, 5, 6, 7, 8, 11. Step 2: Mode: 4 appears three times, more often than any other number, so the mode is 4. Step 3: Median: There are 10 values, so the median is the average of the 5th and 6th values in the sorted list. Step 4: The 5th value is 4 and the 6th value is 5, so median = (4 + 5) / 2 = 4.5. Step 5: Mean: First find the sum of all values: 6 + 3 + 8 + 4 + 3 + 11 + 7 + 4 + 5 + 4 = 55. Step 6: Mean = total sum / number of observations = 55 / 10 = 5.5. Step 7: Sum of mode, median and mean = 4 + 4.5 + 5.5 = 14.

Verification / Alternative check:
Double check each piece: the frequency count clearly shows 4 as the most common value, the sorted positions for median are correct for 10 elements, and the sum 55 is straightforward to verify by grouping (for example, (6 + 4) + (3 + 7) + (8 + 4) + (3 + 5) + (11 + 4) = 10 + 10 + 12 + 8 + 15 = 55).

Why Other Options Are Wrong:
- Option 13.5: This would be the result of a small arithmetic slip when summing 4, 4.5 and 5.5.

- Option 13: This is even lower, inconsistent with the correctly computed values.

- Option 14.5: This would require at least one of the mean, median or mode to be larger than we have calculated.

Common Pitfalls:
Students sometimes confuse the positions for the median when the number of terms is even, or misidentify the mode when several values repeat. Another frequent mistake is in the total sum calculation, which affects the mean. Carefully listing the sorted data and checking each computation reduces such errors.

Final Answer:
The sum of the mode, median and mean for the given data is 14.