The problem asks to find the mean, median, and mode for the given sample of scores:
$5, 4, 5, 2, 7, 1, 3, 5$

1. Mean:

The mean is the average of the numbers. To find it: $\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}}$ Sum of the scores: $5 + 4 + 5 + 2 + 7 + 1 + 3 + 5 = 32$ There are 8 numbers, so the mean is: $\text{Mean} = \frac{32}{8} = 4$

2. Median:

The median is the middle value when the numbers are arranged in ascending order. First, order the numbers: $1, 2, 3, 4, 5, 5, 5, 7$ Since there are 8 numbers (an even number), the median is the average of the two middle numbers (the 4th and 5th values): $\text{Median} = \frac{4 + 5}{2} = 4.5$

3. Mode:

The mode is the number that appears most frequently. From the dataset: $1, 2, 3, 4, 5, 5, 5, 7$ The number 5 appears 3 times, which is more than any other number, so: $\text{Mode} = 5$

Summary:

• Mean: 4
• Median: 4.5
• Mode: 5

Would you like more details or have any questions?

Here are some related questions:

1. What happens if there are two modes in a dataset?
2. How do you calculate the mean if one of the values is negative?
3. Can the median be a value that is not in the dataset?
4. How does an outlier affect the mean compared to the median?
5. Is it possible for the mode to not exist in a dataset?

Tip: The median is less affected by outliers than the mean, making it a better measure of central tendency for skewed distributions.