JAMIA 2022 — Mathematics PYQ

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Question

JAMIA 2022 — Mathematics PYQ

JAMIA | Mathematics | 2022

The median of a set of 9 distinctive observations is 20.5. If each of the largest 4 observations of the set is increased by 2 then the median of the new set

Choose the correct answer:

Explanation

Logical Summary

Original Set (Sorted):

$x_1, x_2, x_3, x_4, \mathbf{x_5}, x_6, x_7, x_8, x_9$

$\text{Median} = x_5 = 20.5$
Modified Set:

The largest 4 observations ( $x_6, x_7, x_8, x_9$ ) are increased by 2.

$x_1, x_2, x_3, x_4, \mathbf{x_5}, (x_6+2), (x_7+2), (x_8+2), (x_9+2)$
Observation:

The 5th value ( $x_5$ ) remains the 5th value because the values being increased were already larger than it. There is no "re-sorting" required that would pull a different number into the 5th position.

Final Answer

The median remains same as that of the original set.