Question

Design a control plan for exam scores for your quality management class.  Describe how you would gather data, what type of chart is needed, how to gather data, how to interpret the data, how to identify causes, and remedial action to be taken when out-of-control situations occur.

Answer 1

Xbar and R chart are the right means to analyse the performance of students in a semester exams. We assume that there are 8 subjects in the exam. The result data can be collected from the examination branch of the institute.  The process is given below.

(i) List the marks of each students column wise. There will be 8 columns.

(ii) Determine the average of each student. also determine the range of marks. Range is the difference between the maximum and the minimum value of the marks of each student.

(iii) Calculate the grand mean ( average of averages) It is Xbarbar.. also calculate the mean range. It is Rbar

(iv) Calculate the upper and lower limits of the Xbar abd R charts with following formulas

UCL_xbar = Xbarbar + A₂*Rbar

LCLxbar = Xbarbar - A₂*Rbar

UCL_R = D₄* Rbar

LCLR= D₃* Rbar

Value of A_2,D3, D₄ can be obtained from standard table.

(v) Identify the students which fall out of these limits in the chart.

The students who fall out of chart in range means the ones who show greater variation among their marks in the examination. Those students are weak in a particular subject which should be addressed to by offering remedial classes or the like. The students who are short on average are either very weak in some, or weak in all of the subjects and should be provided with extra care and higher level of instruction. The test performance can also be used to judge the quality of instruction. Higher number of students out of control limits mean poor quality of instruction, which can further be investigated and corrected.