Question

5 whole numbers are written in order, 4, 6, x, y, 10. The mean and median of the 5 numbers are the same so what are the values of x and y

Answer 1

Answer: The value of x is 7 and the value of y is 8.

Explanation:

It is given that 5 whole numbers are written in order, 4, 6, x, y, 10. The mean and median of the 5 numbers are the same.

$Mean=\frac{\text{Sum of observations}}{\text{No. of observations}}$

$Mean=\frac{4+6+x+y+10}{5}$

$Mean=\frac{20+x+y}{5}$

The 5 numbers are arranged in ascending order. The total numbers are 5 which is odd number so the median is  $(\frac{n+1}{2})_{th}$  term.

n=5

$\frac{n+1}{2}th=\frac{5+1}{2}th=3rd$

The third term is median. So the median is x.

Since mean and median are same.

$\frac{20+x+y}{5}=x$

$20+x+y=5x$

$20=4x-y$     ... (1)

Since the whole numbers are arranged in the ascending order therefore the value of x and y must a whole number greater than 6 and less than 10.

Put x=7 in equation (1).

$20=4(7)-y$

$y=8$

Therefore, the value of x and y are 7 and 8 respectively.

Put x=8.

$20=4(8)-y$

$y=12>10$

Therefore the value of x can not be 8 or not more than that.