find all the modes Score, x	Frequency, f
1	4
2	1
3	6
4	6
5	6
6	5
7	6
8	8

To find the mode(s) of a data set, we look for the score (or value of \(x\)) that appears most frequently, as indicated by the frequency \(f\).

Here’s the dataTo find the mode(s) of a data set, we look for the score (or value of \(x\)) that appears most frequently, as indicated by the frequency \(f\).

Here’s the 

\[
\begin{array}{|c|c|}
\hline
\text{Score } (x) & \text{Frequency } (f) \\
\hline
1 & 4 \\
2 & 1 \\
3 & 6 \\
4 & 6 \\
5 & 6 \\
6 & 5 \\
7 & 6 \\
8 & 8 \\
\hline
\end{array}
\]

Now, let’s examine the frequencies:

- \(f = 4\) for \(x = 1\)
- \(f = 1\) for \(x = 2\)
- \(f = 6\) for \(x = 3, 4, 5, 7\)
- \(f = 5\) for \(x = 6\)
- \(f = 8\) for \(x = 8\)

### Conclusion:
The mode(s) are the value(s) of \(x\) corresponding to the highest frequency, which is 8 for \(x = 8\).

Thus, the mode is **8**.

Would you like further details or have any other questions?

Here are some related questions for you:

1. What if there were two or more scores with the same highest frequency?
2. How do we find the mode in a grouped frequency distribution?
3. Can a data set have no mode?
4. What is the significance of mode in data analysis?
5. How is the mode different from the mean and median?

**Tip:** In multimodal distributions, there can be multiple modes if different values have the same highest frequency.

find all the modes Score, x Frequency, f 1 4 2 1 3 6 4 6 5 6 6 5 7 6 8 8

Learn how to find the mode from a frequency distribution table with scores and frequencies. This problem involves identifying the value(s) with the highest frequency, with a detailed example showing how to determine the mode. Suitable for students in Grades 6-8.

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