Let's calculate the mean, median, and mode for the data set:

Data: $1, 3, 3, 6, 7, 7, 8, 8, 8, 9$

1. Mean

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

$\text{Mean} = \frac{1 + 3 + 3 + 6 + 7 + 7 + 8 + 8 + 8 + 9}{10} = \frac{60}{10} = 6$

So, the mean is $6$.

2. Median

The median is the middle value when the data is ordered from least to greatest. If there is an even number of values, it is the average of the two middle values.

In this case, the ordered data is already: $1, 3, 3, 6, 7, 7, 8, 8, 8, 9$

There are 10 values, so the middle values are the 5th and 6th: $7 \text{ and } 7$

$\text{Median} = \frac{7 + 7}{2} = 7$

So, the median is $7$.

3. Mode

The mode is the value(s) that appear most frequently. In this data set, $8$ appears 3 times, which is more than any other value.

So, the mode is $8$.

Summary:

• Mean = 6
• Median = 7
• Mode = 8

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. What happens if a data set has more than one mode?
2. How is the mean affected by extreme values in the data set?
3. How can the median be useful in interpreting skewed data?
4. What is the difference between the mean and weighted mean?
5. How can the mode be useful in real-life applications?

Tip: When your data set has outliers, the median is often a better representation of central tendency than the mean.