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Whwn mean of observations is 4.4 and variance os 8.24 where 3 observations are 1,2,6 find the ither two observation ?
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Whwn mean of observations is 4.4 and variance os 8.24 where 3 observat...
Let the other two observations be x and y .
Therefore, the series is 1, 2, 6,x,y.
Now Mean x = 4.4 = (1+2+ 6 +x + y) /5
or 22 = 9 + x + y
Therefore
x + y = 13 ... (1)
Also
variance = 8.24 = (1/n) ∑ ( xi - x)2
⇒ 8.24 = (1/5)[ (3.4)2 + (2.4)2 + (1.6)2 + x2 +y2 – 2x(4.4)x (x + y) + 2x(4.4)2]
⇒ 41.20 = 11.56 + 5.76 + 2.56 + x2 + y2 – 8.8 x 13 + 38.72
Therefore x2 + y2 = 97 ….. (2)
But from (1), we have
x2 + y2 + 2xy = 169 …... (3)
From (2) and (3), we have
2xy = 72 ... (4)
Subtracting (4) from (2), we get
x2 + y2 – 2 xy = 97 – 72
i.e. (x– y)2 = 25
or
x – y =+_ 5 ….(5)
So, from (1) and (5), we get
x = 9, y = 4 when
x – y = 5
or
x = 4, y = 9 when x – y = – 5
Thus, the remaining observations are 4 and 9.
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Whwn mean of observations is 4.4 and variance os 8.24 where 3 observations are 1,2,6 find the ither two observation ?
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