The table provides a frequency distribution of scores. To calculate the mean for this set of scores, we can use the formula for the mean of a frequency distribution:

$\text{Mean} = \frac{\sum (x \cdot f)}{\sum f}$

Where:

• $x$ represents the scores,
• $f$ represents the frequency of each score.

Data from the table:

• $x = [5, 4, 3, 2, 1]$
• $f = [1, 1, 2, 5, 1]$

Now let's calculate the mean by following the steps:

1. Multiply each score by its frequency.
2. Sum up these products.
3. Divide the total by the sum of the frequencies.

I'll calculate this now.The mean for the given set of scores in the frequency distribution table is $2.6$.

Would you like more details on how this was calculated, or do you have any other questions? Here are some related questions you might explore:

1. How does the mean change if one of the frequencies increases?
2. What is the median of this data set?
3. How do you calculate the mode in a frequency distribution?
4. Can the mean be lower than the lowest value in a distribution?
5. How would adding more data points affect the mean?

Tip: The mean gives a central tendency, but it doesn't reveal the spread of the data. To understand data variability, you might also want to explore standard deviation or variance.