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  • Statistics when used as a singular sense may be defined as the science of collection, presentation, analysis and interpretation of numerical data
  • In a plural sense, by statistics we mean data relating to any phenomenon that is numerically expressed, enumerated or estimated according to a reasonable standard of accuracy collected in a systematic manner for a pre-determined purpose and placed in relation to each other
  • Data is the quantitative or qualitative information about some particular characteristic(s) under consideration
  • Quantitative characteristic is known as a variable
  • Qualitative characteristic is known as an attribute
  • If the variable assumes finite or a countable infinite number of isolated values, it is known to be discrete variable
  • If the variable assumes any value in a given interval, it is known as continuous variable
  • Collection of data is the method involved in collecting data through censuses and surveys or in a routine manner or through other sources
  • The data which is collected for the first time is known as primary data
  • If already collected data is used for the statistical analysis, it is known as secondary data
  • Methods of collecting primary data
  • Interview method
    • Personal interview method
    • Indirect interview method
    • Mailed questionnaire method
    • Direct observation method
  • Telephonic method
    Important sources of secondary data are
    • Information collected through newspapers and periodicals
    • International sources like WHO, IMF, World Bank
    • Government sources like CSO, ICAI, etc.
  • Checking of the data collected for completeness, accuracy and reliability is known as scrutiny of data.
  • Scrutiny of data means checking of data with the help of related series
  • Classification of data can be categorized as:
    • Chronological (temporal) classification
    • Qualitative (ordinal) classification
    • Geographical (spatial) classification
    • Quantitative (cardinal) classification

      Modes of presentation of data
    • Textual presentation
    • Tabular presentation or tabulation
    • Diagrammatic representation of data
    • Graphical representation of data
  • Textual presentation is not preferred by statisticians at it is dull, monotonous and comparison of data is not possible
  • Attractive representation of statistical data is provided by charts, diagrams and pictures
  • Hidden trend if any in data can be easily noticed by diagrammatic representation
  • When time series exhibit wide range of fluctuations we use logarithmic or ration chart for data analysis
  • Multiple line charts are used for representing two or more related series expressed in same unit
  • Multiple axis charts are used for representing two or more related time series expressed in different unit
  • Horizontal bar diagram: to represent qualitative data or data varying over space
  • Vertical bar diagram: to represent quantitative data or time series data
  • A systematic arrangement which shows how the total frequency is distributed among the different values of variables is called frequency distribution.
  • Types of frequency distribution
  • Discrete frequency distribution: A frequency distribution with discrete variable is called discrete frequency distribution
  • Continuous frequency distribution: A frequency distribution with continuous variable is called continuous frequency distribution
  • The two end values of class intervals are called class limits
  • Class boundaries may be defined as the actual class limit of a class interval. For overlapping or mutually exclusive classification, the class boundaries coincide with the class limits. This is usually applicable for continuous variables
  • For non-overlapping or mutually inclusive classification, which is usually applicable for a discrete variable, we have
    Description: 62152.png 
  • The difference between two successive mid points or the difference between class boundaries is called class width.
  • Range of data is difference between the highest and lowest value of the data
  • Class limit: Class limit is defined as the minimum value and maximum value the class interval may contain.
  • For continuous type data: Class limit = Class boundary
  • For discontinuous type data: Class limit  class boundary
  • Frequency distribution of a single variable is called uni-variate frequency distribution. Frequency distribution of more than one variable is called multi-variate frequency distribution
  • Relative frequency may be defined as the ratio of the class frequency to the total frequency
  • Frequency density may be defined as the ratio of the frequency of that class interval to the corresponding class length
  • Graphical representation of a frequency distribution
    • Histogram or area diagrams
    • Frequency polygon
    • Ogives or cumulative frequency graph
    • Frequency curve
  • Mode can be determined using a histogram
  • If class width are of unequal width, frequency density is used to draw a histogram
  • Frequency curve helps us in understanding the symmetry of the distribution
  • Ogives are cumulative frequency curves

Important Formulae:

  • Description: 62263.png 
  • Midpoint/Mid value/Class mark
  • Width/Size of class = U.C.B – L.C.B
  • Frequency density = Description: 62915.png
  • Relative frequency = Description: 62921.png
  • % frequency = Description: 62927.png × 100

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