Here’s an example of how to calculate mean, median, and mode using a small dataset. Let’s take the following set of numbers:

Data set: 12, 15, 20, 15, 22, 15, 18, 25, 22, 30

1. Mean

The mean is the average of the data set. It is calculated using the formula:

$\text{Mean} = \frac{\sum x_i}{n}$

Where:

• $x_i$ = each data value
• $n$ = number of data values

Computation: $\text{Mean} = \frac{12 + 15 + 20 + 15 + 22 + 15 + 18 + 25 + 22 + 30}{10} = \frac{194}{10} = 19.4$

So, the mean of the data set is 19.4.

2. Median

The median is the middle value when the data set is arranged in order. If there is an odd number of observations, the median is the middle one. If there is an even number of observations, it’s the average of the two middle values.

Steps:

1. Arrange the data in ascending order: 12, 15, 15, 15, 18, 20, 22, 22, 25, 30
2. The data set has 10 values, so the median is the average of the 5th and 6th values: $18$ and $20$.

Computation: $\text{Median} = \frac{18 + 20}{2} = 19$

So, the median of the data set is 19.

3. Mode

The mode is the value that appears most frequently in the data set.

Observation:

• The value 15 appears three times.

So, the mode of the data set is 15.

Summary:

• Mean: 19.4
• Median: 19
• Mode: 15

---

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is the mean, median, and mode of the following set: 5, 8, 10, 8, 12?
2. How do you find the mode if there are multiple values with the same highest frequency?
3. What happens to the mean if one extreme outlier is added to the data set?
4. How does the median help in representing a dataset with outliers?
5. What is the impact of skewed data on mean, median, and mode?

Tip: The mean is sensitive to outliers, while the median provides a better center measure for skewed distributions.