Teachers Work Experience Statistics

The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.

For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2.

A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as $A$ and $B$, where $A < B$. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values:

• Minimum: 2
• Lower Hinge: 6.5
• Median: 12
• Upper Hinge: 21
• Maximum: 29

Which of the following is a possible value of $B$?

Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?

While rechecking her original notes to re-enter the smudged values of $A$ and $B$ in the records, the student found that one of the eleven recorded work experience values that did not get smudged was recorded wrongly as half of its correct value. After re-entering the values of $A$ and $B$, and correcting the wrongly recorded value, she recalculated all the summary measures. The recalculated average value was 15. What is the value of $B$?