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The mean and SD for a, b and 2 are 3 and2÷√3 respectively, The value of ab would be(a) 5 (b) 6(c) 11 (d) 3Please give Full Solution |
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Answer» ab = -5 Step-by-step explanation: The mean and STANDARD deviation for a b and 2 are 3 and 2 √ 3 respectively the VALUE of ab would be Mean = (a + b + 2)/3 = 3 => a + b + 2 = 9 => a + b = 7 Standard deviation = √∑(x - Mean)²/n => 2√3 = √∑(x - Mean)²/n squaring both sides => 12 = ∑(x - Mean)²/n n = 3 => 12 = ∑(x - Mean)²/3 => 36 = ∑(x - Mean)² ∑(x - Mean)² = (a-3)² + (b-3)² + (2-3)² = a² + 9 -6a + b² + 9 - 6b + 1 = a² + b² -6a -6b + 19 equating both a² + b² -6a -6b + 19 = 36 using a² + b² = (a + b)² - 2ab => (a+b)² - 2ab - 6(a+b) + 19 = 36 putting value of a + b = 7 => 7² - 2ab - 6(7) = 17 => 49 - 2ab - 42 = 17 => -2ab = 10 => ab = -5 |
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