Answer:
x = 3
Step-by-step explanation:
Given mean group data:
- [tex]8,11,8,10,6,7,3x,11,11[/tex]
To find the value of x we simply add the total ages by combining like terms divided by the sum of data set which gives us 9 years.
[tex]\dotfill[/tex]
[tex]\\\boxed{\begin{array}{l}\underline{\textsf{Mean Group}}\\\\\sf \frac{8+11+8+10+6+7+3x+11+11}{9}=9\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$8+11+8+10+6+7+3x+11+11$ is the dataset.}\\\phantom{ww}\bullet\;\textsf{9 - (Denominator) is the number of dataset.}\\\phantom{ww}\bullet\;\textsf{9 - (RHS) is the known average of the dataset with the unknown(x)}\end{array}}[/tex]
Steps:
- Cross-multiply the equation
[tex]\frac{8+11+8+10+6+7+3x+11+11}{9}=9[/tex]
[tex]8+11+8+10+6+7+3x+11+11=9 \times 9[/tex]
- Comine like terms
[tex]8+11+8+10+6+7+3x+11+11=81[/tex]
[tex](8+11+8+10+6+7+11+11)+3x=81[/tex]
- Add values
[tex]3x + 72 = 81[/tex]
- Substract 72 from both sides
[tex]3x = 81 - 72[/tex]
[tex]3x = 9[/tex]
[tex]x = \frac{9}{3}[/tex]
[tex]x=3[/tex]
Therefore, the value of x simplifies to:
[tex]\boxed{ \boxed{x=3}}[/tex]
