The average of five consecutive numbers is x. If the next two numbers are included, how shall the average vary?

The average of five consecutive numbers is x. If the next two numbers are included, how shall the average vary? Correct Answer It shall increase by 1

Let the five consecutive numbers be z, z + 1, z + 3 and z + 4
Then,
$$ \Rightarrow \frac{{z + \left( {z + 1} \right) + \left( {z + 2} \right) + \left( {z + 3} \right) + \left( {z + 4} \right)}}{5} = x$$
$$\eqalign{ & \Rightarrow 5z + 10 = 5x \cr & \Rightarrow z = \frac{{5x - 10}}{5} \cr & \Rightarrow z = x - 2 \cr} $$
So, the numbers are x - 2, x - 1, x, x + 1, x + 2
∴ Required mean
$$ = \frac{{\left( {x - 2} \right) + \left( {x - 1} \right) + x + \left( {x + 1} \right) + \left( {x + 2} \right) + \left( {x + 3} \right) + \left( {x + 4} \right)}}{7}$$
$$\eqalign{ & = \frac{{7x + 7}}{7} \cr & = x + 1 \cr} $$
Bissoy MCQ

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