To find the mean, median, and mode of the data set:
$8, 12, 32, 10, 3, 4, 4, 4, 4, 5, 12, 20$

1. Mean (average):

To find the mean, sum up all the numbers, then divide by the total number of values.

$\text{Mean} = \frac{8 + 12 + 32 + 10 + 3 + 4 + 4 + 4 + 4 + 5 + 12 + 20}{12}$

$\text{Mean} = \frac{118}{12} \approx 9.83$

2. Median (middle value):

To find the median, first arrange the numbers in ascending order:

$3, 4, 4, 4, 4, 5, 8, 10, 12, 12, 20, 32$

Since there are 12 values (an even number), the median will be the average of the 6th and 7th values. These values are 5 and 8.

$\text{Median} = \frac{5 + 8}{2} = \frac{13}{2} = 6.5$

3. Mode (most frequent value):

The mode is the value that appears most often. In this case, 4 appears four times.

$\text{Mode} = 4$

Summary:

• Mean: 9.83
• Median: 6.5
• Mode: 4

Would you like further clarification or details? Here are five questions to explore:

1. How does the mean change if the largest value (32) is removed?
2. What happens to the mode if another number appears four times?
3. Can a data set have more than one mode?
4. Why is the median less sensitive to outliers than the mean?
5. How would adding a very large number affect the mean, median, and mode?

Tip: The median is particularly useful for skewed data sets because it isn't influenced by extreme values.