Question

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 about 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.

Accepted Answer

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

Answer

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

Answer

(P) rightarrow (5), (Q) rightarrow (2), (R) rightarrow (3), (S) rightarrow

Answer

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

${{\text{X}}_{\text{i}}}$	${{f}_{\text{i}}}$	$\begin{gathered}M=6 \\ e_i=\left\\|x_i-M\right\\|\end{gathered}$	$\text{M}=6$ ${{\text{e}}_{\text{i}}}=\left\\| {{\text{x}}_{\text{i}}}-\text{M} \right\\|$	$\sum {{f}_{\text{i}}}{{\text{d}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}{{\text{e}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}\text{d}_{\text{i}}^{2}$
4	5	3	2	15	10	45
5	4	2	1	8	4	16
6	1	1	0	1	0	1
8	3	1	2	3	6	3
9	2	2	3	4	6	8
11	3	4	5	12	15	48
12	1	5	6	5	6	25
				48	47	146

JEE Advanced 2025 — Paper 1 — Question 28

Answer: C

${{\text{X}}_{\text{i}}}$	${{f}_{\text{i}}}$	$\begin{gathered}M=6 \\ e_i=\left\\|x_i-M\right\\|\end{gathered}$	$\text{M}=6$ ${{\text{e}}_{\text{i}}}=\left\\| {{\text{x}}_{\text{i}}}-\text{M} \right\\|$	$\sum {{f}_{\text{i}}}{{\text{d}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}{{\text{e}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}\text{d}_{\text{i}}^{2}$
4	5	3	2	15	10	45
5	4	2	1	8	4	16
6	1	1	0	1	0	1
8	3	1	2	3	6	3
9	2	2	3	4	6	8
11	3	4	5	12	15	48
12	1	5	6	5	6	25
				48	47	146

${{\text{X}}_{\text{i}}}$	${{f}_{\text{i}}}$	$\begin{gathered}M=6 \\ e_i=\left\\|x_i-M\right\\|\end{gathered}$	$\text{M}=6$ ${{\text{e}}_{\text{i}}}=\left\\| {{\text{x}}_{\text{i}}}-\text{M} \right\\|$	$\sum {{f}_{\text{i}}}{{\text{d}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}{{\text{e}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}\text{d}_{\text{i}}^{2}$
4	5	3	2	15	10	45
5	4	2	1	8	4	16
6	1	1	0	1	0	1
8	3	1	2	3	6	3
9	2	2	3	4	6	8
11	3	4	5	12	15	48
12	1	5	6	5	6	25
				48	47	146

${{\text{X}}_{\text{i}}}$	${{f}_{\text{i}}}$	$\begin{gathered}M=6 \\ e_i=\left\\|x_i-M\right\\|\end{gathered}$	$\text{M}=6$ ${{\text{e}}_{\text{i}}}=\left\\| {{\text{x}}_{\text{i}}}-\text{M} \right\\|$	$\sum {{f}_{\text{i}}}{{\text{d}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}{{\text{e}}_{\text{i}}}$	$\sum {{f}_{\text{i}}}\text{d}_{\text{i}}^{2}$
4	5	3	2	15	10	45
5	4	2	1	8	4	16
6	1	1	0	1	0	1
8	3	1	2	3	6	3
9	2	2	3	4	6	8
11	3	4	5	12	15	48
12	1	5	6	5	6	25
				48	47	146