Here are the definitions and examples of mean, median, and mode:

1. Mean (Average)

The mean is the sum of all values divided by the number of values. It gives the central value of a dataset by "averaging" the values.

Formula:
$\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}$

Example: Consider the dataset: 5, 10, 15, 20, 25.
To find the mean: $\text{Mean} = \frac{5 + 10 + 15 + 20 + 25}{5} = \frac{75}{5} = 15$ So, the mean is 15.

2. Median

The median is the middle value in a dataset when it is ordered in ascending or descending order. If the number of values is odd, the median is the middle number. If the number is even, it’s the average of the two middle numbers.

Example: Consider the dataset: 5, 10, 15, 20, 25.
Since the dataset has 5 values (an odd number), the median is the middle value: 15.

If we have an even number of values, say, 5, 10, 15, 20, 25, 30: $\text{Median} = \frac{15 + 20}{2} = 17.5$ So, the median is 17.5.

3. Mode

The mode is the value(s) that appear most frequently in a dataset. A dataset can have one mode, more than one mode, or no mode if all values are unique.

Example: Consider the dataset: 5, 10, 15, 10, 25.
In this case, 10 appears most frequently, so the mode is 10.

If the dataset were: 5, 10, 15, 10, 25, 15: Both 10 and 15 appear twice, so the modes are 10 and 15 (making it bimodal).

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Would you like further details or have any questions?

Here are some additional questions for exploration:

1. How do you calculate the mean of a larger dataset with outliers?
2. How do the mean and median compare in a skewed dataset?
3. Can a dataset have no mode? Provide an example.
4. How do you calculate the median for grouped data?
5. What are some real-life applications of mean, median, and mode?

Tip: For datasets with outliers, the median is often a better measure of central tendency than the mean.