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Standard IX

Mathematics

Mean

If the mean o...

Question

If the mean of x, y, z is y, then mean of x and z is ________.

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Solution

It is given that the mean of x, y, z is y.

$∴ \frac{x + y + z}{3} = y (Mean = \frac{Sum of observations}{Total number of observations}) \Rightarrow x + y + z = 3 y \Rightarrow x + z = 3 y - y = 2 y . . . . . (1)$

Mean of x and z $= \frac{x + z}{2} = \frac{2 y}{2} = y$ [Using (1)]

If the mean of x, y, z is y, then mean of x and z is y.

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If the mean of x, y, z is y, then mean of x and z is ________.

It is given that the mean of x, y, z is y. ∴x+y+z3=y Mean=Sum of observationsTotal number of observations⇒x+y+z=3y⇒x+z=3y-y=2y .....1 Mean of x and z =x+z2=2y2=y [Using (1)] If the mean of x, y, z is y, then mean of x and z is ____y____.