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

1. Mean:

   • Definition: The mean, or average, is the sum of all values in a data set divided by the number of values.
   • Example: Suppose we have the data set: $2, 4, 6, 8, 10$.
     • Sum of values: $2 + 4 + 6 + 8 + 10 = 30$
     • Number of values: $5$
     • Mean = $\frac{30}{5} = 6$.

2. Median:

   • Definition: The median is the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle numbers.
   • Example: With the data set $1, 3, 7, 9, 15$:
     • Arranged in order, the middle value (3rd position) is $7$.
     • Therefore, the median is $7$.
     • For an even-numbered data set, say $1, 3, 7, 9$, the median is the average of $3$ and $7$: $\frac{3 + 7}{2} = 5$.

3. Mode:

   • Definition: The mode is the value(s) that appears most frequently in a data set. A set can have one mode, more than one mode, or no mode if all values are unique.
   • Example: In the data set $2, 4, 4, 6, 8$:
     • The value $4$ appears twice, which is more frequent than any other number.
     • Thus, the mode is $4$.

These are fundamental concepts in statistics that provide insights into different aspects of data.

Would you like more details or have any questions?

Here are 5 related questions to further explore these concepts:

1. How would you calculate the mean if some values in the data set are negative?
2. What happens to the median if you add a new value to the data set?
3. Can a data set have more than one mode? If yes, provide an example.
4. How does an outlier in the data set affect the mean, median, and mode?
5. Why might the median be preferred over the mean in certain situations?

Tip: When dealing with data skewed by outliers, the median often gives a better central measure than the mean.