1- Descriptive Statistics:
Summary:Summarizing and interpreting data using measures of central tendency, variability, and distribution.- Definition: Descriptive statistics involve summarizing and describing the main features of a dataset.
- Measures of Central Tendency: Mean (average), median (middle value), and mode (most frequent value).
- Measures of Variability: Range (difference between the highest and lowest values), variance (average of squared deviations from the mean), and standard deviation (square root of variance).
- Distribution: Describes how data values are spread or clustered (e.g., normal distribution, skewness, kurtosis).
- Usage: Provides a simple summary of the data, making it easier to understand and interpret.
- Advantages: Facilitates quick insights into the data’s characteristics.
- Examples: Calculating the average age of customers, the range of exam scores, and visualizing data distribution with histograms.
2- Inferential Statistics:
Summary: Making predictions or inferences about a population based on a sample using hypothesis testing and confidence intervals.- Definition: Inferential statistics use a sample of data to make inferences or predictions about a larger population.
- Hypothesis Testing: A method for testing a hypothesis about a parameter in a population using sample data. It involves formulating null (no effect) and alternative (some effect) hypotheses, and using test statistics to determine the likelihood of the hypotheses.
- Confidence Intervals: A range of values derived from sample data that is likely to contain the true population parameter. It provides an estimate of the uncertainty around the sample estimate.
- Usage: Helps in making generalizations and decisions based on sample data.
- Advantages: Allows for conclusions about populations without needing to survey every individual.
- Examples: Estimating the average height of a population, testing the effectiveness of a new drug, and determining the reliability of manufacturing processes.