JEE Advanced · Mathematics · 20. Statistics

Consider the given data with frequency distribution $\begin{array}{l} x_{i} & 3 & 8 & 11 & 10 & 5 & 4 \\ f_{i} & 5 & 2 & 3 & 2 & 4 & 4 \end{array}$ Match each entry in List-I to the correct entries in List-II.

List-I List-II

$(P)$ The mean of the above data is $(1)$ $2.5$

$(Q)$ The median of the above data is $(2)$ $5$

$(R)$ The mean deviation about the
mean of the above data is $(3)$ $6$

$(S)$ The mean deviation about the
median of the above data is $(4)$ $2.7$

$(5)$ $2.4$

The correct option is

A $(P) \to (3) (Q) \to (2) (R) \to (4) (S) \to (5)$
B $(P) \to (3) (Q) \to (2) (R) \to (1) (S) \to (5)$
C $(P) \to (2) (Q) \to (3) (R) \to (4) (S) \to (1)$
D $(P) \to (3) (Q) \to (3) (R) \to (5) (S) \to (5)$

Verified Solution

Answer & Solution

Correct Answer

(A) $(P) \to (3) (Q) \to (2) (R) \to (4) (S) \to (5)$

Step-by-step Solution

Detailed explanation

Arranging the given data in ascending order we get,

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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	List-I		List-II
$(P)$	The mean of the above data is	$(1)$	$2.5$
$(Q)$	The median of the above data is	$(2)$	$5$
$(R)$	The mean deviation about the mean of the above data is	$(3)$	$6$
$(S)$	The mean deviation about the median of the above data is	$(4)$	$2.7$
		$(5)$	$2.4$