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defon
3 years ago
10

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 o

f x and y
Mathematics
1 answer:
Volgvan3 years ago
3 0

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.

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