Statistics (Class 11 Mathematics)

• Introduction

  • Definition of Statistics
  • Primary objective: Analysis of quantitative data
  • Limitations: Deals with aggregates, not individuals

• Measures of Dispersion

  • Need for Dispersion
    • Mean alone is insufficient
    • Measures how data is spread out
  • Range
    • Difference between maximum and minimum observations
  • Mean Deviation
    • Definition: Average of absolute deviations from a central value
    • Mean Deviation about Mean
      • For ungrouped data
      • For grouped data (discrete and continuous)
    • Mean Deviation about Median
      • For ungrouped data
      • For grouped data
  • Variance
    • Definition: Average of squared deviations from the mean ($\sigma^2$)
    • Formula for ungrouped data
    • Formula for discrete frequency distribution
    • Formula for continuous frequency distribution (sub-group data)
  • Standard Deviation
    • Definition: Positive square root of variance ($\sigma$)
    • Formula and properties

• Analysis of Frequency Distributions

  • Comparing Variability
    • Two distributions with same mean may have different variability
  • Coefficient of Variation (C.V.)
    • Definition: Ratio of standard deviation to mean, expressed as percentage
    • Formula: $C.V. = \frac{\sigma}{\bar{x}} \times 100$
    • Utility: Comparing consistency of two or more data sets (less C.V. means more consistent)