IDNLearn.com provides a collaborative environment for finding and sharing knowledge. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.

Find the mean for the data items in the given frequency distribution.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
Score, $x$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
Frequency, $f$ & 3 & 5 & 6 & 3 & 3 & 3 & 5 & 2 \\
\hline
\end{tabular}
\][/tex]

The mean is [tex]$\square$[/tex] (Round to 3 decimal places as needed.)


Sagot :

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].