Statistical Data Analysis and Interpretation

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Introduction
The old adage ‘what gets measured improves’ is reflected in the dramatic increase in the range and scope of data being collected today. We are barraged with statistics on sports results, economic indicators and politics: people are becoming familiar with scoring averages, inflation rates and voter satisfaction surveys. The advent of low-cost personal computers combined with the widespread availability of powerful computing software, such as Excel, means that many people have both large data sets and powerful tools with which to analyse them. In this report, a data set collected by the author, in an observational study, is analysed. The data set contains three variables; Project Score; the score accumulated by each student prior to sitting the end of term exam. Attendance Score; calculated as a percentage of term lectures attended. Final Score; the score accumulated by each student and calculated using the weighted average of the project and exam scores. The analysis considers a variety of different methods to represent and reduce the data-set, the results presented are discussed briefly and the most appropriate family of measures for the data-set identified. Organisation providing Data Source

The University of Limerick was established in 1972 as the National Institute for Higher Education: Limerick, and achieved university classification in 1989. The university, now in its 40th year, provides graduate and postgraduate education to over eleven thousand students. Students are offered a wide range of modules, delivered by teaching staff in the twenty-eight departments spread across four faculties. An important function of the teaching staff is the grading of student submissions and the calculation of final grades. The university gives discretion to teaching staff in respect of these tasks, enabling them to determine how best to assess student learning. It is important that staff reduce and represent grading data in a manner that ensures learning outcomes are met. In this report, the data set is taken from grading results of a module delivered by the author to third year students of the Construction Management and Engineering programme - LM082. The module is delivered in thirteen contact-weeks and is assessed via a project and an end of semester exam, accounting for 30% and 70% of the final score, respectively. Presentation of Data-Set

The data-set used in this report was collected in a single academic semester and has been ‘denatured’ to obscure the students’ identity. The data-set is presented in Table 1 and contains fifty elements, one for each student - identified by ID 1 through 50. Student Score Table

The presentation of the score table presents the first opportunity to consider how best to represent the data-set. A student score table is ordinarily presented in alphabetic order of student name. In this report, the data-set is represented in rank order of ascending final-score. This arrangement allows the reader to observe important parameters such as; maximum, minimum, range, mode and median, final scores directly from the table.

TABLE 1: STUDENT SCORE DATA SET USED IN REPORT.
Arranging the data in this order will also make some of the graphs produced easier to interpret.
Grading Schema
The student grade is calculated by applying a grading schema to the final score. The schema defines the number of classes used and the width of each class. Teaching staff have discretion and can modify the schema to suit the module needs. One version recommended by our department is presented in Table 2. It can be seen from the table that the departmental schema uses a non-uniform class interval.

TABLE 2: DEPARTMENTAL AND UNIFORM GRADING SCHEMA.
In this report, we will demonstrate how the impact of different grading schema can best be viewed using standard statistical methods. To this end, an alternative ‘uniform’ schema is generated and presented in Table 2. Finally, the table presents a...
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