To find the mean for the given frequency distribution, follow these steps:
1. List the scores and their corresponding frequencies:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
\text{Score, } x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\text{Frequency, } f & 3 & 5 & 6 & 3 & 3 & 3 & 5 & 2 \\
\hline
\end{array}
\][/tex]
2. Find the sum of the product of each score and its corresponding frequency:
[tex]\[
\sum (x \cdot f) = (1 \cdot 3) + (2 \cdot 5) + (3 \cdot 6) + (4 \cdot 3) + (5 \cdot 3) + (6 \cdot 3) + (7 \cdot 5) + (8 \cdot 2)
\][/tex]
[tex]\[
= 3 + 10 + 18 + 12 + 15 + 18 + 35 + 16 = 127
\][/tex]
3. Find the total frequency:
[tex]\[
\sum f = 3 + 5 + 6 + 3 + 3 + 3 + 5 + 2 = 30
\][/tex]
4. Calculate the mean:
[tex]\[
\text{Mean} = \frac{\sum (x \cdot f)}{\sum f} = \frac{127}{30}
\][/tex]
5. Round the mean to three decimal places:
[tex]\[
\frac{127}{30} \approx 4.233
\][/tex]
So, the mean of the given frequency distribution is [tex]\( \boxed{4.233} \)[/tex].
