Sure, let's find the mean age of the four girls step by step.
1. Convert each age into months:
- For the girl aged 6 years 3 months:
[tex]\[
6 \text{ years} \times 12 \text{ months/year} + 3 \text{ months} = 72 \text{ months} + 3 \text{ months} = 75 \text{ months}
\][/tex]
- For the girl aged 5 years 7 months:
[tex]\[
5 \text{ years} \times 12 \text{ months/year} + 7 \text{ months} = 60 \text{ months} + 7 \text{ months} = 67 \text{ months}
\][/tex]
- For the girl aged 7 years 0 months:
[tex]\[
7 \text{ years} \times 12 \text{ months/year} + 0 \text{ months} = 84 \text{ months}
\][/tex]
- For the girl aged 9 years 2 months:
[tex]\[
9 \text{ years} \times 12 \text{ months/year} + 2 \text{ months} = 108 \text{ months} + 2 \text{ months} = 110 \text{ months}
\][/tex]
So, we have the ages in months as follows:
[tex]\[
75 \text{ months}, 67 \text{ months}, 84 \text{ months}, 110 \text{ months}
\][/tex]
2. Calculate the mean age in months:
- Sum of the ages in months:
[tex]\[
75 + 67 + 84 + 110 = 336 \text{ months}
\][/tex]
- The mean age in months is:
[tex]\[
\frac{336 \text{ months}}{4} = 84 \text{ months}
\][/tex]
3. Convert the mean age back to years and months:
- To convert 84 months into years and months, note that there are 12 months in a year.
- The number of full years in 84 months is:
[tex]\[
\left\lfloor \frac{84}{12} \right\rfloor = 7 \text{ years}
\][/tex]
The remaining months after accounting for the full years:
[tex]\[
84 \text{ months} \mod 12 = 0 \text{ months}
\][/tex]
So, the mean age of the four girls is 7 years 0 months.
