If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and ${{20} \over 3}$, respectively, then the value of | a $-$ b | is equal to :
Solution
$10 = {{7 + 10 + 11 + 15 + a + b} \over 6}$<br><br>$\Rightarrow$ a + b = 17 ..... (i)<br><br>$${{20} \over 3} = {{{7^2} + {{10}^2} + {{11}^2} + {{15}^2} + {a^2} + {b^2}} \over 6} - {10^2}$$<br><br>a<sup>2</sup> + b<sup>2</sup> = 145 ...... (ii)<br><br>Solve (i) and (ii) a = 9, b = 8 or a = 8, b = 9<br><br>| a $-$ b | = 1
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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