Answer:
13, 11, 4, 16, 6, 22
Step-by-step explanation:
<em>Let the second digit be x and the last digit be y</em>
Given:
- Data set: 13, x, 4, 16, 6, y
- Mean = 12
- y = 2x or x = 2y
The mean of the data is the average. The average can be calculated by determining the sum of the terms and dividing it by the total digits.
![\implies \text{Mean of data:} \ \dfrac{13 + x + 4 + 16 + 6 + y}{6} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BMean%20of%20data%3A%7D%20%5C%20%5Cdfrac%7B13%20%2B%20x%20%2B%204%20%2B%2016%20%2B%206%20%2B%20y%7D%7B6%7D%20%3D%2012)
Let us substitute the value of y (2x) in the data.
![\implies \dfrac{13 + x + 4 + 16 + 6 + 2x}{6} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B13%20%2B%20x%20%2B%204%20%2B%2016%20%2B%206%20%2B%202x%7D%7B6%7D%20%3D%2012)
Now, add all the terms in the data and simplify.
![\implies \dfrac{39 + x +2x}{6} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B39%20%2B%20x%20%2B2x%7D%7B6%7D%20%3D%2012)
![\implies \dfrac{39 + 3x}{6} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B39%20%2B%203x%7D%7B6%7D%20%3D%2012)
Distribute the denominators and simplify.
![\implies \dfrac{39}{6} + \dfrac{3x}{6} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B39%7D%7B6%7D%20%2B%20%5Cdfrac%7B3x%7D%7B6%7D%20%20%3D%2012)
![\implies \dfrac{13}{2} + \dfrac{x}{2} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%20%5Cdfrac%7B13%7D%7B2%7D%20%2B%20%5Cdfrac%7Bx%7D%7B2%7D%20%20%3D%2012)
![\implies 6.5 + \dfrac{x}{2} = 12](https://tex.z-dn.net/?f=%5Cimplies%20%206.5%20%2B%20%5Cdfrac%7Bx%7D%7B2%7D%20%20%3D%2012)
Subtract 6.5 both sides and simplify.
![\implies 6.5 + \dfrac{x}{2} - 6.5 = 12 - 6.5](https://tex.z-dn.net/?f=%5Cimplies%20%206.5%20%2B%20%5Cdfrac%7Bx%7D%7B2%7D%20%20-%206.5%20%3D%2012%20-%206.5)
![\implies \dfrac{x}{2} = 5.5](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bx%7D%7B2%7D%20%3D%205.5)
Use cross multiplication and simplify.
![\implies x= 5.5 \times 2](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%205.5%20%5Ctimes%202)
![\implies x= 11](https://tex.z-dn.net/?f=%5Cimplies%20%20x%3D%2011)
To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".
![\implies y = 2x](https://tex.z-dn.net/?f=%5Cimplies%20y%20%3D%202x)
![\implies y = 2(11)](https://tex.z-dn.net/?f=%5Cimplies%20y%20%3D%202%2811%29)
![\implies y = 22](https://tex.z-dn.net/?f=%5Cimplies%20y%20%3D%2022)
When the x and y values are substituted in the data, we get;
Therefore, the data is 13, 11, 4, 16, 6, 22.