dispression

• Measures of Dispersion indicate the extent to which individual items in a series are scattered about an average.
• General Classification of Measures of Dispersion

  1. Measures of Absolute Dispersion
  2. Measures of Relative Dispersion
• Measures of absolute dispersion are expressed in the units of the original observations.
• Measures of absolute dispersion cannot be used to compare variations of two data sets when the averages of these data sets differ a lot in value or when the observations differ in units of measurement
• range of set measurements is the difference between the largest and the smallest values.
• Range – defined as the difference of the highest observed value and the lowest observed value
• standard deviation is the most frequently used measure of dispersion
• variance is not a measure of absolute dispersion.
• variance is not expressed in the same units as the original observations
• Standard Deviation is affected by the value of every observation. It may be distorted by few extreme values.
• Standard Deviation can not be computed from an open-ended distribution.
• coefficient of variation is the ratio of the standard deviation to the mean and is usually expressed in percentage
• standard score measures how many standard deviations an observation is above or below the mean.
• standard score is not a measures of relative dispersion per se but is somewhat related
• standard score is useful for comparing two values from different series specially when these two series differ with respect to the mean of standard deviation or both are expressed in different units
• measure of skewness shows the degree of asymmetry, or departure from symmetry of a distribution..
• measure of skewness indicates not only the amount of skewness but also the direction
• Two Type of Skewness

  1. Positively Skewed or Skewed to the right
  2. Negatively Skewed or Skewed to the Left
• Positively Skewed or Skewed to the right

  • distribution tapers more to the right than to the left

  • longer tail to the right

  •more concentration of values below than above the mean

  • most skewed curves encountered in the social sciences are skewed to the right.
• Negatively Skewed or Skewed to the Left

  • distribution tapers more to the left than to the right

  • longer tail to the left

  • more concentration of values above than below the mean

  •only rarely do we find curves skewed to the left, and even more rarely do we find data characteristically skewed to the left