Measures of Dispersion

  • Introduction to Measure of Dispersion

    A modern student of statistics is mainly interested in the study of variability and uncertainty. In this section we shall discuss variability and its measures and uncertainty will be discussed in probability. We live in a changing world. Changes are taking place in every sphere of life. A man of statistics does not show much […]

  • Measures of Dispersion

    For the study of dispersion, we need some measures which show whether the dispersion is small or large. There are two types of measure of dispersion which are: (a) Absolute Measure of Dispersion (b) Relative Measure of Dispersion Absolute Measures of Dispersion: These measures give us an idea about the amount of dispersion in a […]

  • Range and Coefficient of Range

    The Range: Range is defined as the difference between the maximum and the minimum observation of the given data. If denotes the maximum observation denotes the minimum observation then the range is defined as In case of grouped data, the range is the difference between the upper boundary of the highest class and the lower […]

  • Quartile Deviation and its Coefficient

    Quartile Deviation: It is based on the lower quartile and the upper quartile . The difference is called the inter quartile range. The difference   divided by is called semi-inter-quartile range or the quartile deviation. Thus The quartile deviation is a slightly better measure of absolute dispersion than the range. But it ignores the observation […]

  • Mean Deviation and its Coefficient

    The mean deviation or the average deviation is defined as the mean of the absolute deviations of observations from some suitable average which may be the arithmetic mean, the median or the mode. The difference is called deviation and when we ignore the negative sign, this deviation is written as and is read as mod […]

  • Standard Deviation

    The standard deviation is defined as the positive square root of the mean of the square deviations taken from arithmetic mean of the data. For the sample data the standard deviation is denoted by and is defined as:                         For frequency distribution the formulas becomes                            The standard deviation is in the same units […]

  • Examples of Standard Deviation

     Examples of Standard Deviation: This tutorial is about some examples of standard deviation using all methods which are discussed in the pervious tutorial. Example: Calculate the standard deviation for the following sample data using all methods: 2, 4, 8, 6, 10, and 12. Solution:             Method-I: Actual Mean Method               Method-II: Taking Assumed Mean […]

  • Coefficient of Standard Deviation and Variation

    Coefficient of Standard Deviation: The standard deviation is the absolute measure of dispersion. Its relative measure is called standard coefficient of dispersion or coefficient of standard deviation. It is defined as: Coefficient of Variation: The most important of all the relative measure of dispersion is the coefficient of variation. This word is variation not variance. […]

  • Uses of Coefficient of Variation

    Uses of Coefficient of Variation: Coefficient of variation is used to know the consistency of the data. By consistency we mean the uniformity in the values of the data/distribution from arithmetic mean of the data/distribution. A distribution with smaller than the other is taken as more consistent than the other. is also very useful when […]

  • The Variance

    Variance is another absolute measure of dispersion. It is defined as the average of the squared difference between each of the observations in a set of data and the mean. For a sample data the variance is denoted is denoted by and the population variance is denoted by (sigma square). The sample variance has the […]

  • Sheppard Corrections and Corrected Coefficient of Variation

    Sheppard Corrections: In grouped data the different observations are put into the same class. In the calculation of variation or standard deviation for grouped data, the frequency is multiplied with which is the mid-point of the respective class. Thus it is assumed that all the observations in a class are centered at . But this […]

  • Combined Variance

    Like combined mean, the combined variance or standard deviation can be calculated for different sets of data. Suppose we have two sets of data containing and observations with means and , and variances and . If is the combined mean and is the combined variance of observations, then combined variance is given by It can […]