Let's solve the problem step-by-step to find the average number of movies watched by students during one week. We'll use the frequency distribution table provided.
The table is as follows:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Movies Watched in a Week} & \text{Tally} & \text{Frequency} \\
\hline
6 & 1 & 1 \\
\hline
5 & & 0 \\
\hline
4 & \text{III} & 3 \\
\hline
3 & \text{III III I} & 8 \\
\hline
2 & \text{II I} & 6 \\
\hline
1 & \text{II} & 2 \\
\hline
0 & \text{III} & 3 \\
\hline
\end{array}
\][/tex]
1. Calculate the total number of students:
Sum the frequencies listed in the table:
[tex]\[
1 + 0 + 3 + 8 + 6 + 2 + 3 = 23
\][/tex]
Thus, the total number of students is [tex]\(23\)[/tex].
2. Calculate the total number of movies watched:
Multiply each number of movies watched by its corresponding frequency and then sum these products:
[tex]\[
(6 \times 1) + (5 \times 0) + (4 \times 3) + (3 \times 8) + (2 \times 6) + (1 \times 2) + (0 \times 3)
\][/tex]
[tex]\[
= 6 + 0 + 12 + 24 + 12 + 2 + 0 = 56
\][/tex]
Thus, the total number of movies watched is [tex]\(56\)[/tex].
3. Calculate the average (mean) number of movies watched:
Divide the total number of movies watched by the total number of students:
[tex]\[
\text{Average} = \frac{\text{Total number of movies watched}}{\text{Total number of students}} = \frac{56}{23} \approx 2.4347826086956523
\][/tex]
4. Round the average to the nearest hundredth:
To round the average to the nearest hundredth, we look at the third decimal place:
[tex]\[
2.4347826086956523 \approx 2.43
\][/tex]
Therefore, the average number of movies watched by students during one week is approximately [tex]\(2.43\)[/tex] when rounded to the nearest hundredth.
