Question

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

Answer 1

From the information above we can arrange the terms in descending or ascending order in order to get the median.

Since :

a < b < c

In an ascending order we have :

x + a, x + b, x + c

The median is the term at the middle which is x + b.

The mean = { ( x + a) + ( x + b) + ( x + c)} ÷ 3

(3x + a + b + c) / 3 = mean

From the question : mean = median

x + b = ( 3x + a + b + c) / 3

3x + 3b = 3x + a + b + c

Collecting like terms together :

3x - 3x + 3b - b = a + c

2b = a + c

b = ( a + c) /2

From the mean equated to mean we can get the value of c in terms of a and b:

2b - a = c

Writing be in terms of a and b:

b = { a + (2b - a)} / 2

This is the answer.

Answer 2

Answer:

b={a+(2b-a)}/2

Step-by-step explanation:

since

a<b<c

{(x+a)+(x+b)+(x+c)}/3

(3x+a+b+c)/3

x+b=(3x+a+b+c)/3

3x+3b=3x+a+b+c

2b=a+c

b=(a+c)/2

2b-a=c

b={a+(2b-a)}/2