सांख्यिकी Chapter 1: वर्णनात्मक सांख्यिकी

Descriptive Statistics

• Measures of Central Tendency:
  • Mean (average value)
  • Median (middle value when data is in order)
  • Mode (most frequent value)
• Measures of Variability:
  • Range (difference between largest and smallest values)
  • Interquartile Range (IQR, difference between Q3 and Q1)
  • Variance (average of squared differences from mean)
  • Standard Deviation (square root of variance)

Inferential Statistics

• Hypothesis Testing:
  • Null Hypothesis (H0): a statement of no effect or no difference
  • Alternative Hypothesis (H1): a statement of an effect or difference
  • Test Statistic: a value calculated from sample data
  • P-Value: probability of obtaining the test statistic (or more extreme) assuming H0 is true
• Confidence Intervals:
  • A range of values within which a population parameter is likely to lie
  • Margin of Error: the maximum amount by which the sample statistic may differ from the population parameter

Probability

• Basic Concepts:
  • Experiment: an action or situation that can produce a set of outcomes
  • Sample Space: the set of all possible outcomes
  • Event: a set of one or more outcomes of an experiment
• Rules of Probability:
  • The probability of an event is a number between 0 and 1
  • The probability of the sample space is 1
  • The probability of the empty set is 0
  • The probability of an event is equal to 1 minus the probability of its complement

Data Visualization

• Types of Plots:
  • Histogram: a graphical representation of a distribution
  • Box Plot: a graphical representation of a dataset's distribution and outliers
  • Scatter Plot: a graphical representation of the relationship between two variables
• Data Visualization Best Practices:
  • Clearly label axes and provide a title
  • Avoid 3D plots and excessive use of color
  • Use plots to show patterns and relationships, not just to display data