InterviewSolution
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InterviewSolution
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The mean and variance of five observations are 6 and 4 respectively. If threeof these are 5, 7 and 9, find the other two observations. |
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Answer» Let remaining two observations are x and y.We know, Mean = sum of observations/total number of observations ⇒6 = (5 + 7 + 9 + x + y)/5⇒6*5 = 21+ (x + y) ⇒ 30 - 21 = (x + y) ⇒ (x + y) = 9------(1) Variance of given observations is 4we know, variance is given Variance = sum of (observation - mean) ^2 /total number of observations 4= {(5 - 6)² + (7 - 6)² + (9 - 6)² + (x - 6)² + (y - 6)²}/54*5 = (-1)² + (1)² + (3)² + x² + y² - 12(x + y) + 6² + 6² 20 = 1 + 1 + 9 + x² + y² - 12*9 + 36 + 36 20 = 83 + x² + y² - 108x² + y² = 128 - 83x² + y² = 45 ------(2) Solve equations (1) and (2), x² + (9 - x)² = 45x² + 81 + x² - 18x = 452x² -18x + 36 = 0x² - 9x + 18 = 0 (x - 6)(x - 3) = 0x = 6, 3 put it in equation (1) Then, y = 9 - 6 = 3 or y = 9 - 3 = 6 Hence, remaining two observations are 3, 6 |
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