{"id":211,"date":"2019-08-01T08:44:59","date_gmt":"2019-08-01T08:44:59","guid":{"rendered":"http:\/\/hsp16.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=211"},"modified":"2019-08-01T08:45:42","modified_gmt":"2019-08-01T08:45:42","slug":"measures-of-dispersion-i","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/hsp16\/chapter\/measures-of-dispersion-i\/","title":{"rendered":"Measures of Dispersion – I"},"content":{"raw":"
\r\n

1. Introduction<\/strong><\/p>\r\n \r\n

In a series, all the items are not equal. There is difference of variation among the values. The degree of variation is evaluated by various measures of dispersion. \u201cThe degree to which numerical data tend to spread about an average value is called the<\/p>\r\n \r\n

\u201cVariation or dispersion of the data\u201d. It means that the deviation of each individual values around the measures of central values. If the value of dispersion is less it implies more reliability of the averages. If the value of dispersion is higher, it will not represent the averages. It is less reliable. Otherwise the measure of central value will not represent the individual values. In this module we are going to discuss range, mean deviation and quartile deviation alone.<\/strong><\/p>\r\n \r\n

2. Objectives<\/strong><\/p>\r\n \r\n

In this module, the following aspects of measures of dispersion are to be discussed along with percentile as it is directly used to calculate Kelly\u2019s co efficient of skewness.<\/p>\r\n\r\n

    \r\n \t
  1. Percentile<\/li>\r\n \t
  2. Importance or significance of measures of dispersion<\/li>\r\n \t
  3. Criteria or characteristics or desirable properties of a measure of dispersion<\/li>\r\n \t
  4. Absolute and Relative Measures<\/li>\r\n \t
  5. Range<\/li>\r\n \t
  6. Quartile Deviation<\/li>\r\n<\/ol>\r\n

    3.Percentiles What is percentile?<\/strong><\/p>\r\n \r\n

    P1, P2, P3\u2026.. P99\u00a0 are the ninety nine percentiles. They divide a series into 100\u00a0<\/span>equal parts.<\/span><\/p>\r\n \r\n

    Formulae: <\/strong>There are ninety nine percentiles. Instead of considering the formula for each percentile, the method and the formula for kth percentile are considered. The required formula can be obtained from it by substituting k = 1,2,3,\u2026.99.<\/span><\/p>\r\n \r\n

    In\u00a0 Individual\u00a0 observations\u00a0 and\u00a0 Discrete\u00a0 Series,\u00a0 Pk\u00a0 is\u00a0 the\u00a0 value\u00a0 of\u00a0 an\u00a0 item\u00a0 at\u00a0\u00a0<\/span>k(N+1)th\u00a0<\/span>41(N+1)th\u00a0<\/span>position. For example, P41 is the value of the item at\u00a0<\/span>position when\u00a0<\/span>100\u00a0 <\/span>100\u00a0<\/span>all the items are in ascending order. In Continuous Series, the continuous class interval in which kN\/100th item is included and identified by considering the class intervals in ascending order. After identifying the percentile class, the following formula is used to calculate median.<\/span><\/p>\r\n\r\n<\/div>\r\n

    \u00a0 \u00a0ik( kN \u2212cfk)<\/p>\r\n

    Pk = Lk + [\u00a0 \u00a0100\u00a0 ]<\/p>\r\n

    fk<\/p>\r\n \r\n

    The subscript k may not be necessary if L, cf, f and I are identified properly for each particular Pk while calculating more than Pk.<\/p>\r\n\"\"<\/a>\r\n\r\n\"\"<\/a>\r\n

    \r\n

    4.\u00a0<\/strong>Importance or Significance of Measures of Dispersion <\/strong>Dispersion is measured for the following purposes:<\/p>\r\n \r\n

      \r\n \t
    1. Firstly,the reliability of a measure of central tendency is known through measure of dispersion.<\/li>\r\n \t
    2. Secondly,measures of Dispersion provide a basis for the control of variability.<\/li>\r\n \t
    3. Thirdly, they help to compare two or more sets of data with regard to their variability.<\/li>\r\n \t
    4. Fourthly, they enhance the utility and scope of statistical techniques.<\/li>\r\n \t
    5. Criteria or desirable properties of a measure of dispersion<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      \r\n