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The mean of 5 observations is 44 and variance is 8.24. If three of the five observations are 1,2 and 6, find the other two.

Asked by shivamaggarwal363663 | 02 Oct, 2021, 13:30: PM

Expert Answer

Let the two numbers be x and y

As the mean is 4.4, we have

rightwards double arrow fraction numerator 1 plus 2 plus 6 plus straight x plus straight y over denominator 5 end fraction equals 4.4 rightwards double arrow 9 plus straight x plus straight y equals 22 rightwards double arrow straight x plus straight y equals 13 space space... space left parenthesis straight i right parenthesis As space variance space equals space 8.24 rightwards double arrow fraction numerator 1 squared plus 2 squared plus 6 squared plus straight x squared plus straight y squared over denominator 5 end fraction minus open parentheses 4.4 close parentheses equals 8.24 rightwards double arrow straight x squared plus straight y squared equals 138 minus 41 rightwards double arrow straight x squared plus straight y squared equals 97 space space... space left parenthesis ii right parenthesis Using space left parenthesis straight i right parenthesis space in space left parenthesis ii right parenthesis comma space we space get straight x squared plus open parentheses 13 minus straight x close parentheses squared equals 97 rightwards double arrow straight x squared plus 169 plus straight x squared minus 26 straight x equals 97 rightwards double arrow straight x squared minus 13 straight x plus 36 equals 0 rightwards double arrow straight x equals 4 comma 9 When space straight x equals 4 comma space then space straight y equals 9 When space straight x equals 9 comma space then space straight y equals 4

Answered by Renu Varma | 21 Oct, 2021, 12:46: PM

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