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JEE Class main Answered

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, 01:30: 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
JEE main - Maths
Asked by shivamaggarwal363663 | 02 Oct, 2021, 01:30: PM
ANSWERED BY EXPERT
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