Question

The mean and median of the data x+a, x+b, x+c are equal and "a" less than "b" is less than "c" then find the value of "b" in the term of "a" and "b"

Answer 1

Since, 3 values are given so n=3
Median of odd number of terms = value of term at [ ( n + 1 ) / 2 ]th position
Median = value at [ ( 3 + 1 )/2 ]th position
Median = value at [ 4 /2 ]th position
Median = value at 2nd position
Median = x + b

Mean = ( sum of all values ) / ( no. of values )
Mean = ( x+a + x+b + x+c ) / 3
Mean = ( 3x+a+b+c ) / 3

Since, mean and median are equal so,
x + b = ( 3x+a+b+c ) / 3
3x + 3b = 3x + a + b + c
3b = a + b + c
2b = a + c
b = ( a + c ) / 2