Question

the mean and median of the data is x+a ,x + b, x + c are equal and a< b <c then find the value of c in terms of a and b​

Answer 1

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$\sf{data : (x + a),(x + b),(x + c)} \\ \sf{no. \: of \: observations \: are \: 3, \: i.e. \: odd} \\ \sf{median \: calculated \: will \: be \: for \: odd \: observations}$

$\sf{for \: the \: given \: data : } \\ \sf{mean = median}$

$\sf{ \frac{(x + a) + (x + b) + (x + c)}{3} = ( \frac{3 + 1 }{2})th \: observation } \\ \sf{ \frac{3x + a + b + c}{3} = ( \frac{4}{2} )th} \\ \sf{ \frac{3x + a + b + c}{3} = (2)th } \\ \sf{ \frac{3x + a + b + c}{3} = x + b} \\ \sf{3x + a + b + c = 3x + 3b} \\ \sf{ \cancel{3x} + a + b + c = \cancel{3x} + 3b} \\ \sf{a + b + c = 3b} \\ \sf{c = 3b - b - a} \\ \boxed{\sf{c = 2b - a}}$

Answer 2

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