Question

The numbers: 1, 2, X, 11, 7, and 14 are in ascending order the mean is 8 and the median is 9. Find the value of Xand Y​

Answer 1

x = 7

y = 13

Explanation:

We are told that the numbers 1, 2, x, 11, y, 14 are in ascending order.

Therefore, x must be somewhere between 2 and 11, and y must be somewhere between 11 and 14.

`\hrulefill`

Median

The median is the middle value of a data set when all the data values are placed in order of size.

There are 6 numbers in the data set. As this is an even number of data values, the median is the mean of the middle two data values, i.e. the mean of the numbers in 3rd and 4th position.

The two data values in 3rd and 4th position are x and 11.

Given the median is 9, we can set up the following equation and solve for x:

`\begin{aligned}(x+11)/(2)&=9\\\\2 \cdot (x+11)/(2)&=2 \cdot 9\\\\ x+11&=18\\\\x+11-11&=18-11\\\\x&=7\end{aligned}`

Therefore, the value of x is 7.

`\hrulefill`

Mean

The mean of a data set is the sum of the data values divided by the number of data values. Therefore, if the mean is 8, we can set up the following equation:

`(1+2+x+11+y+14)/(6)=8`

Substitute the found value of x into the equation, and solve for y:

`\begin{aligned}(1+2+7+11+y+14)/(6)&=8\\\\(y+35)/(6)&=8\\\\6 \cdot (y+35)/(6)&=6 \cdot 8\\\\y+35&=48\\\\y+35-35&=48-35\\\\y&=13\end{aligned}`

Therefore, the value of y is 13.