Before You Begin
Question #40592
The Question
A dataset is formed by the following process: For every possible non-empty selection of items from a collection of 3 identical red, 3 identical blue, and 3 identical green balls, the total number of balls in the selection is recorded as a data point in . Let be the minimum possible value of the mean deviation of about any real number . Find the value of .
Options
- A.
97
- B.
98
- C.
102
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Specialist
Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.
Concepts Behind This Question
Total Selection (at least one)|Selection from Identical Items|Mean Deviation about Mean vs. Median|Standard Deviation and Coefficient of Variation
Why This Question Is Tricky
Common Mistakes
This question tests the intersection of combinatorics and statistics.
The primary trap lies in the statistical property of mean deviation: students often mechanically calculate it about the mean (which yields 682/7) rather than the median.
Furthermore, the combinatorial setup forces an asymmetric distribution by excluding the empty selection.
If a student forgets to exclude the empty selection, the distribution becomes perfectly symmetric (Mean = Median = 4.5), which bypasses the intended statistical trap and leads to an incorrect sum of 102.
Quick Facts About This Question
Question Information
| Subject | Mathematics |
| Chapter | Permutations and Combinations - Class 11 |
| Concept | Total Selection (at least one) |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |