JEE Main 2026 — Statistics Question with Solution
JEE Main 2026 (28 January Shift 1)
Question
The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are , then the mean deviation about the median of all the 10 observations is
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Show full solutionCorrect option: C
Correct answer
C5
Step-by-step explanation
Given 10 observations with mean = 9 and variance = 34.2.
Eight known values: 2, 3, 5, 10, 11, 13, 15, 21.
Sum of all 10: .
Sum of 8 known: 80. So the two unknowns sum to 10.
From variance: .
Sum of squares of 8 known: 1094. So unknown squares sum to 58.
With and : we get , giving roots , so the unknowns are 3 and 7.
All 10 sorted: 2, 3, 3, 5, 7, 7, 10, 11, 13, 15, 21.
Median = .
Mean deviation =
Eight known values: 2, 3, 5, 10, 11, 13, 15, 21.
Sum of all 10: .
Sum of 8 known: 80. So the two unknowns sum to 10.
From variance: .
Sum of squares of 8 known: 1094. So unknown squares sum to 58.
With and : we get , giving roots , so the unknowns are 3 and 7.
All 10 sorted: 2, 3, 3, 5, 7, 7, 10, 11, 13, 15, 21.
Median = .
Mean deviation =
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This is a previous-year question from JEE Main 2026, covering the Statistics chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.