If the mean and variance of six observations 7,10,11,15,a,b are 10 and 20/3, respectively, then the value of |a-b| is equal to:

Correct answer: (D) 1. Given: Mean=10 ⇒(7+10+11+15+a+b)/6=10 ⇒a+b=17 …i And, Variance=20/3 ⇒(7^2+10^2+11^2+15^2+a^2+b^2)/6-10^2=20/3 ⇒(495+a^2+b^2)/6=320/3 ⇒495+a^2+b^2=640 ⇒a^2+b^2=145 …ii Solve i and ii, we get a=9, b=8 or a=8, b=9 ∴a-b=1

Q45 / 90 · JEE Main 2021 (20 Jul Shift 2) · Mathematics

If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3},$ respectively, then the value of $| a - b |$ is equal to:

A
$9$
B
$11$
C
$7$
Correct answer
D
$1$

Solution

Given:

Mean $= 10$

$\Rightarrow \frac{7 + 10 + 11 + 15 + a + b}{6} = 10$

$\Rightarrow a + b = 17 \dots (i)$

And,

Variance $= \frac{20}{3}$

$\Rightarrow \frac{7^{2} + 10^{2} + 11^{2} + 15^{2} + a^{2} + b^{2}}{6} - 10^{2} = \frac{20}{3}$

$\Rightarrow \frac{495 + a^{2} + b^{2}}{6} = \frac{320}{3}$

$\Rightarrow 495 + a^{2} + b^{2} = 640$

$\Rightarrow a^{2} + b^{2} = 145 \dots (ii)$

Solve $(i)$ and $(i i)$ , we get

$a = 9, b = 8$ or $a = 8, b = 9$

$∴ |a - b| = 1$

Hence, the correct answer is option: 'D'.

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If the mean and variance of six observations 7,10,11,15,a,b are 10 and 203, respectively, then the value of |a-b| is equal to:

Solution

Relevant Questions

If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3},$ respectively, then the value of $| a - b |$ is equal to: