Consider the following frequency distribution: Value 4 5 8 9 6 12 11 Frequency 5 f_1 f_2 2 1 1 3 Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For the given frequency distribution, let \alpha denote the mean deviation about the mean, \beta denote the mean deviation a the median, and \sigma^2 denote the variance. Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) 7 f_1+9 f_2 is equal to (1) 146 (Q) 19 \alpha is equal to (2) 47 (R) 19 \beta is equal to (3) 48 (S) 19 \alpha^2 is equal to (4) 145 (5) 55 [JEE Adv 2025 P1]

Correct Answer is : (P) ⟶ (5) (Q) ⟶ (3) (R) ⟶ (2) (S) ⟶ (1)

(P) \rightarrow (5) (Q) \rightarrow (3) (R) \rightarrow (2) (S) \rightarrow (4)

(P) \rightarrow (5) (Q) \rightarrow (2) (R) \rightarrow (3) (S) \rightarrow (1)

(P) \rightarrow (5) (Q) \rightarrow (3) (R) \rightarrow (2) (S) \rightarrow (1)

(P) \rightarrow (3) (Q) \rightarrow (2) (R) \rightarrow (5) (S) \rightarrow (4)

Statistics

Section: Mathematics

Question : 1 of 2

Marks: +1, -0

Consider the following frequency distribution:

Value	4	5	8	9	6	12	11
Frequency	5	f1	f2	2	1	1	3

Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6.
For the given frequency distribution, let α denote the mean deviation about the mean, β denote the mean deviation a the median, and σ2 denote the variance.
Match each entry in List-I to the correct entry in List-II and choose the correct option.

	List-I		List-II
(P)	7f1+9f2 is equal to	(1)	146
(Q)	19α is equal to	(2)	47
(R)	19β is equal to	(3)	48
(S)	19α2 is equal to	(4)	145
		(5)	55

[JEE Adv 2025 P1]

(P) ⟶ (5) (Q) ⟶ (3) (R) ⟶ (2) (S) ⟶ (4)
(P) ⟶ (5) (Q) ⟶ (2) (R) ⟶ (3) (S) ⟶ (1)
(P) ⟶ (5) (Q) ⟶ (3) (R) ⟶ (2) (S) ⟶ (1)
(P) ⟶ (3) (Q) ⟶ (2) (R) ⟶ (5) (S) ⟶ (4)

Validate

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Value (xi)	fi	cf	fixi
4	5	5	20
5	f1	5+f1	20
6	1	6+f1	6
8	f2	6+f1+f2	24
9	2	8+f1+f2	18
11	3	11+f1+f2	33
12	1	12+f1+f2	12