Respuesta :
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.
[tex]Mean=\frac{\text{Sum of observations}}{\text{No. of observations}}[/tex]
[tex]Mean=\frac{4+6+x+y+10}{5}[/tex]
[tex]Mean=\frac{20+x+y}{5}[/tex]
The 5 numbers are arranged in ascending order. The total numbers are 5 which is odd number so the median is [tex](\frac{n+1}{2})_{th}[/tex] term.
n=5
[tex]\frac{n+1}{2}th=\frac{5+1}{2}th=3rd[/tex]
The third term is median. So the median is x.
Since mean and median are same.
[tex]\frac{20+x+y}{5}=x[/tex]
[tex]20+x+y=5x[/tex]
[tex]20=4x-y[/tex] ... (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).
[tex]20=4(7)-y[/tex]
[tex]y=8[/tex]
Therefore, the value of x and y are 7 and 8 respectively.
Put x=8.
[tex]20=4(8)-y[/tex]
[tex]y=12>10[/tex]
Therefore the value of x can not be 8 or not more than that.
