Let's calculate the mean, median, and mode of the given set of numbers: $5, 0, 1, 5, 5, 3, 3, 1$.

1. Mean:

The mean is the sum of all numbers divided by the total number of values.

$\text{Mean} = \frac{5 + 0 + 1 + 5 + 5 + 3 + 3 + 1}{8} = \frac{23}{8} = 2.875$

2. Median:

The median is the middle value of the numbers when they are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.

Arranged in ascending order: $0, 1, 1, 3, 3, 5, 5, 5$.

There are 8 values, so we take the average of the 4th and 5th values: $\text{Median} = \frac{3 + 3}{2} = 3$

3. Mode:

The mode is the value that appears most frequently in the data set.

From the list $5, 0, 1, 5, 5, 3, 3, 1$, the number 5 appears 3 times, and the number 1 appears 2 times. So, 5 is the mode.

Summary:

• Mean: 2.875
• Median: 3
• Mode: 5

Do you need more explanation on any of these?

Here are some related questions:

1. How does the median differ from the mean in datasets with extreme values?
2. How do you find the mode in a set where multiple numbers have the same frequency?
3. Can there be more than one mode? If so, what is it called?
4. What is the significance of the mean in real-world data analysis?
5. How would you handle outliers when calculating the mean?

Tip: When calculating the mean, always check for outliers that might skew the result.