If the mean and variance of six observations 7,10,11,15,a,b are10 and 203 respectively, then the value of a-bis equal to

∵ Mean =10 = 7+10+11+15+a+b6=10⇒a+b=17………..(i) variance = 20/3⇒72+102+112+152+a2+b26=203⇒a2+b2=145...............(ii)From (1) and (ii), a = 9, b = 8 or a = 8, b = 9|a – b| = 1

If the mean and variance of six observations 7,10,11,15,a,b are10 and 203 respectively, then the value of a-bis equal to

∵ Mean =10 = 7+10+11+15+a+b6=10⇒a+b=17………..(i) variance = 20/3⇒72+102+112+152+a2+b26=203⇒a2+b2=145...............(ii)From (1) and (ii), a = 9, b = 8 or a = 8, b = 9|a – b| = 1

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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

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Detailed Solution

$∵$ Mean =10 = $\frac{7 + 10 + 11 + 15 + a + b}{6} = 10$
$\Rightarrow a + b = 17$ ………..(i)
variance = 20/3
$\Rightarrow \frac{7^{2} + 10^{2} + 11^{2} + 15^{2} + a^{2} + b^{2}}{6} = \frac{20}{3}$
$\Rightarrow a^{2} + b^{2} = 145............... (i i)$
From (1) and (ii), a = 9, b = 8 or a = 8, b = 9
|a – b| = 1