Modified Methods of Computing Some Descriptive Statistics for Grouped Data

Abstract

In this paper, a method that approximates the individual observations in a grouped frequency distribution is presented. This approximation provides an alternative method for computing descriptive statistics like the mean, variance and the mean absolute deviation about the median and also opens up the data to further statistical analysis. In particular, the method for calculating the mean absolute deviation about the median bypasses the absolute operator and provides a new way of assessing dispersion in grouped frequency distributions. The performance of the proposed method was assessed via the mean squared error, mean absolute
percentage error and the Kolmogorov-Smirnov test. The descriptive statistics obtained through the proposed method were compared with the Brazauskas-Serfling method, using real-life data and simulated data. The results showed that the proposed method yields a good fit when evaluated against the ungrouped original observations and competed favourably with the Brazauskas-Serfling method, as the values of the performance metrics were equal in most cases. The proposed method therefore provides a way to assess the goodness-of-fit of a grouped data against any hypothesized distribution, as well as provide an estimate of the mean absolute deviation about the median for grouped frequency distributions.