Consider a data consisting of 10 observations $\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots, \mathrm{x}_{10}$, whose mean is 5 and variance is 7 . If the mean and the variance of the first 8 observations $\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots, \mathrm{x}_{8}$ are 4 and 3.5, respectively, and $\mathrm{x}_{9}<\mathrm{x}_{10}$, then the value of $3 \mathrm{x}_{9}+2 \mathrm{x}_{10}$ is ____.

Statistics — JEE Advanced · 2026 · 17 May 2026 · Paper 2 Question with Solution

Consider a data consisting of 10 observations

x_{1}, x_{2}, \dots, x_{10}

, whose mean is 5 and variance is 7 . If the mean and the variance of the first 8 observations

x_{1}, x_{2}, \dots, x_{8}

are 4 and 3.5, respectively, and

x_{9} < x_{10}

, then the value of

3 x_{9} + 2 x_{10}

is ____.

Answer: 44

From the 10 observations:

\sum_{i = 1}^{10} x_{i} = 50

and

\sum_{i = 1}^{10} x_{i}^{2} = 320

. From the first 8:

\sum_{i = 1}^{8} x_{i} = 32

and

\sum_{i = 1}^{8} x_{i}^{2} = 156

. Thus

x_{9} + x_{10} = 18

and

x_{9}^{2} + x_{10}^{2} = 164

. Solving:

x_{9}^{2} + (18 - x_{9})^{2} = 164 \Rightarrow x_{9}^{2} - 18 x_{9} + 80 = 0 \Rightarrow x_{9} = 8

10

. Since

x_{9} < x_{10}

x_{9} = 8, x_{10} = 10

. Therefore

3 x_{9} + 2 x_{10} = 24 + 20 = 44

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Numerical answer

Value	4	5	8	9	6	12	11
Frequency	5	$f_{1}$	$f_{2}$	2	1	1	3

Value

Frequency

f_{1}

f_{2}

$x_{i}$	3	8	11	10	5	4
$f_{i}$	5	2	3	2	4	4

x_{i}

f_{i}