Chapter: Statistics

• Introduction to Statistics

  • Meaning of Statistics (Collection, presentation, analysis, and interpretation of data)
  • Role in daily life and decision-making

• Collection of Data

  • Primary Data
    • Collected directly by the investigator for a specific purpose
    • Example: Asking classmates about their favorite sport
  • Secondary Data
    • Collected by someone else and used later by the investigator
    • Example: Data from newspapers or TV channels

• Presentation of Data

  • Raw Data
    • Unorganized initial data collected
  • Frequency Distribution Table
    • Ungrouped frequency distribution
    • Grouped frequency distribution (using Class Intervals, Lower Limit, Upper Limit)
  • Key terms: Range (Difference between maximum and minimum values), Class Size, Class Mark

• Graphical Representation of Data

  • Bar Graph
    • Pictorial representation with bars of uniform width
  • Histogram
    • Area diagrams representing grouped frequency distributions (continuous classes)
  • Frequency Polygon
    • Drawn by joining mid-points of the tops of rectangle bars in a histogram or using class marks

• Measures of Central Tendency

  • Mean ($\bar{x}$)
    • Average of all observations
    • Formula for ungrouped data: $\frac{\text{Sum of all observations}}{\text{Total number of observations}}$ ($\frac{\sum x_i}{n}$)
  • Median
    • Middle-most value of the data arranged in ascending/descending order
    • Odd number of observations: Value of $\left(\frac{n+1}{2}\right)^{\text{th}}$ term
    • Even number of observations: Average of $\left(\frac{n}{2}\right)^{\text{th}}$ and $\left(\frac{n}{2}+1\right)^{\text{th}}$ terms
  • Mode
    • Value that occurs most frequently (maximum frequency)
    • Can be unimodal, bimodal, or multimodal