XAT 2024 QADI Solutions | DI Set - Upper hinge of Data Set | XAT 2024 | 2IIM CAT Preparation

Question: 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 the 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 is less than 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
Q1) Which of the following is a possible value of B?
A. 13
B. 8
C. 29
D. 6
E. 2
Q2) Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?
A. 13.5
B. 12.5
C. 12
D. 14
E. 13

Hello folks!
DI sets from XAT are usually known to be scoring questions - here's one set from the XAT DI. This DI set on Upper Hinge of Data Set is broadly from statistics. Do watch the video fully to practice XAT Set theory!

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