Statistics For Data Science

Concept: Hypothesis testing is a statistical framework used to evaluate assumptions about a population using sample data. It helps determine whether observed results are statistically significant or due to random chance. Step 1: {\color{red}What is a Hypothesis Test?}
A hypothesis test involves:

• Formulating assumptions about a population
• Using sample data to evaluate those assumptions
• Making a decision using statistical evidence

Step 2: {\color{red}Null Hypothesis ( )}
The null hypothesis represents:

• No effect, no difference, or status quo
• A baseline assumption to test against

Example: A new drug has no effect compared to the old one.
Step 3: {\color{red}Alternative Hypothesis ( or )}
The alternative hypothesis represents:

• A significant effect or difference
• What the researcher aims to support

Example: The new drug is more effective than the old one.
Step 4: {\color{red}Decision Making}
Based on statistical evidence:

• Reject if strong evidence exists
• Fail to reject if evidence is insufficient

Step 5: {\color{red}Importance}
Hypothesis testing is widely used in:

• Scientific research
• A/B testing
• Quality control and data analysis

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: where:

• = data values
• = 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 is odd → middle value
• If 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