Question

Please answer this with explanation. Please I really am struggling. I will mark you brainalist. Please solve it Please

Answer 1

13, 11, 4, 16, 6, 22

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.

`\implies \text{Mean of data:} \ (13 + x + 4 + 16 + 6 + y)/(6) = 12`

Let us substitute the value of y (2x) in the data.

`\implies (13 + x + 4 + 16 + 6 + 2x)/(6) = 12`

Now, add all the terms in the data and simplify.

`\implies (39 + x +2x)/(6) = 12`

`\implies (39 + 3x)/(6) = 12`

Distribute the denominators and simplify.

`\implies (39)/(6) + (3x)/(6) = 12`

`\implies (13)/(2) + (x)/(2) = 12`

`\implies 6.5 + (x)/(2) = 12`

Subtract 6.5 both sides and simplify.

`\implies 6.5 + (x)/(2) - 6.5 = 12 - 6.5`

`\implies (x)/(2) = 5.5`

Use cross multiplication and simplify.

`\implies x= 5.5 * 2`

`\implies x= 11`

To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".

`\implies y = 2x`

`\implies y = 2(11)`

`\implies y = 22`

When the x and y values are substituted in the data, we get;

• ⇒ 13, 11, 4, 16, 6, 22

Therefore, the data is 13, 11, 4, 16, 6, 22.