Question

Define Mean, Median, and Mode and explain which is most affected by outliers.

Hint:

Outliers distort the mean the most, while the median remains stable and is preferred for skewed data.

Answer 1

Concept: Mean, median, and mode are measures of central tendency used to summarize a dataset. Each provides a different perspective on the typical value depending on data distribution. Step 1: {\color{red}Mean}
The mean is the arithmetic average: \[ \text{Mean} = \frac{\sum x_i}{n} \] where:

• $x_i$ = data values
• $n$ = number of observations

It uses all values in the dataset.
Step 2: {\color{red}Median}
The median is the middle value when data is sorted:

• If $n$ is odd → middle value
• If $n$ is even → average of two middle values

It is less sensitive to extreme values.
Step 3: {\color{red}Mode}
The mode is the most frequently occurring value:

• A dataset may have one, multiple, or no modes

It is useful for categorical data.
Step 4: {\color{red}Effect of Outliers}
Outliers are extreme values that differ significantly from others:

• Mean is highly affected (uses all values)
• Median is resistant to outliers
• Mode is usually unaffected

Step 5: {\color{red}Conclusion}
Among the three measures:

• Mean changes significantly with outliers
• Median is the most robust