To compute the mean, median, and mode for the given data set, we need to follow these steps:

Data Set:

$7, 1, 1, 0, 5, 6, 1, 13, 2, 0, 1, 12, 1, 1$

1. Mean:

The mean is calculated by summing all the values and then dividing by the number of values.

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

Sum of all values:

$7 + 1 + 1 + 0 + 5 + 6 + 1 + 13 + 2 + 0 + 1 + 12 + 1 + 1 = 51$

Number of values:

$\text{Number of values} = 14$

$\text{Mean} = \frac{51}{14} \approx 3.6429$

2. Median:

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

Sorted Data Set:

$0, 0, 1, 1, 1, 1, 1, 2, 5, 6, 7, 12, 13$

Since there are 14 numbers (an even number), the median will be the average of the 7th and 8th values:

$\text{Median} = \frac{1 + 2}{2} = \frac{3}{2} = 1.5$

3. Mode:

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

Frequency of each number:

• 0: 2 times
• 1: 5 times
• 2: 1 time
• 5: 1 time
• 6: 1 time
• 7: 1 time
• 12: 1 time
• 13: 1 time

Mode:

The number "1" appears the most frequently, 5 times. Therefore, the mode is 1.

Final Answers:

• Mean: $\approx 3.6429$
• Median: $1.5$
• Mode: $1$

Would you like more details on any of these calculations or have any questions?

Here are some additional related questions to explore:

1. What is the range of the data set?
2. How would the mean change if an outlier is added to the data set?
3. What is the variance of the data set?
4. How is the mode affected by adding or removing values in the data set?
5. What is the difference between mean and median in skewed data?

Tip: The mean is sensitive to extreme values, so in datasets with outliers, the median is often a better measure of central tendency.