Answer:
13, 11, 4, 16, 6, 22
Step-by-step explanation:
Let the second digit be x and the last digit be y
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.
[tex]\implies \text{Mean of data:} \ \dfrac{13 + x + 4 + 16 + 6 + y}{6} = 12[/tex]
Let us substitute the value of y (2x) in the data.
[tex]\implies \dfrac{13 + x + 4 + 16 + 6 + 2x}{6} = 12[/tex]
Now, add all the terms in the data and simplify.
[tex]\implies \dfrac{39 + x +2x}{6} = 12[/tex]
[tex]\implies \dfrac{39 + 3x}{6} = 12[/tex]
Distribute the denominators and simplify.
[tex]\implies \dfrac{39}{6} + \dfrac{3x}{6} = 12[/tex]
[tex]\implies \dfrac{13}{2} + \dfrac{x}{2} = 12[/tex]
[tex]\implies 6.5 + \dfrac{x}{2} = 12[/tex]
Subtract 6.5 both sides and simplify.
[tex]\implies 6.5 + \dfrac{x}{2} - 6.5 = 12 - 6.5[/tex]
[tex]\implies \dfrac{x}{2} = 5.5[/tex]
Use cross multiplication and simplify.
[tex]\implies x= 5.5 \times 2[/tex]
[tex]\implies x= 11[/tex]
To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".
[tex]\implies y = 2x[/tex]
[tex]\implies y = 2(11)[/tex]
[tex]\implies y = 22[/tex]
When the x and y values are substituted in the data, we get;
Therefore, the data is 13, 11, 4, 16, 6, 22.
