Certainly! Here are the definitions of mean, median, and mode, along with examples for each:

1. Mean (Average)

The mean is the sum of all the numbers in a data set divided by the count of numbers in that set. It represents the "average" value.

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

Example:
Consider the data set: $5, 10, 15, 20, 25$.

1. Sum of values: $5 + 10 + 15 + 20 + 25 = 75$
2. Count of values: $5$
3. Mean: $\frac{75}{5} = 15$

So, the mean is 15.

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2. Median

The median is the middle value in an ordered data set. If there’s an odd number of values, the median is the exact middle value. If there’s an even number of values, it’s the average of the two middle values.

Example: Using the data set: $3, 8, 12, 17, 24$ (which is already in order).

• Since there are 5 values (an odd number), the middle value is the third one: 12.

If the data set was: $3, 8, 12, 17, 24, 30$ (6 values, even number), the median would be the average of the two middle values (12 and 17): $\text{Median} = \frac{12 + 17}{2} = 14.5$

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3. Mode

The mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode at all if all values are unique.

Example:
For the data set: $4, 1, 2, 4, 3, 4, 5$,

• The mode is 4, as it appears three times, which is more frequent than any other number.

If the data set were $1, 2, 2, 3, 4, 4, 5$, it would have two modes, 2 and 4, because both appear twice.

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Would you like further details or have any questions?

Related Questions:

1. How are mean, median, and mode different in terms of sensitivity to outliers?
2. Can the mean, median, and mode be the same for a given data set?
3. How is the median calculated in a large data set?
4. What are the real-life applications of mean, median, and mode?
5. How does the mode change if no value is repeated?

Tip: The median is often preferred for skewed data, as it better represents the central tendency when outliers are present.