Descriptive Statistics

• Descriptive statistics summarizes, organizes, and presents data informatively.
• The main objective is to describe the key characteristics of a dataset.
• This is done without drawing conclusions about a larger population.

Types of Variables

• Qualitative variables cannot be measured numerically.
  • Nominal variables are categories without order (e.g., eye color).
  • Ordinal variables are categories with order (e.g., satisfaction level).
• Quantitative variables can be measured numerically.
  • Discrete variables have integer values (e.g., number of children).
  • Continuous variables have decimal values (e.g., height, weight).

Measures of Central Tendency

• Arithmetic Mean: The average of the data.
  • The formula is: $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$
• Median: The central value of the ordered data.
• Mode: The value that appears most frequently.

Measures of Dispersion

• Range: Difference between the maximum and minimum values.
• Variance: Average of the squared differences of each data point from the mean.
  • The formula is: $\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}$
• Standard Deviation: Square root of the variance.
  • The formula is: $\sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}}$

Graphical Representations

• Bar Graph: For qualitative or discrete quantitative variables.
• Histogram: For continuous quantitative variables.
• Pie Chart: To represent proportions.
• Scatter Plot: To visualize the relationship between two variables.

Example

• The ages of 5 people: 20, 22, 25, 28, 30 are analyzed.
  • Mean: (20 + 22 + 25 + 28 + 30) / 5 = 25
  • Median: 25
  • Range: 30 - 20 = 10

Conclusion

• Descriptive statistics provides essential tools for understanding and communicating information from data.