In the normal distribution, half the scores fall below mean and remaining half fall above the mean; which means that 50% of the students scored below the mean and the 50% students scored above the mean. Although, that’s not the case in the given example. In this case, 75% of students scored below the mean and remaining 25% students scored above the mean. Since, the normal curve is perfectly symmetrical, we would have to consider only 25% above mean and 25% below mean students for the given example to be a normal distribution.
Although it is evident that this is not a normal distribution, to evaluate whether or not to curve exam scores, instructor should find out standard deviation for this distribution of the exam scores. If three standard deviations below the mean and three standard deviations above the mean score covers 99.72% (Approximately 100%) of the students; then the instructor can curve the exam scores. In normal bell shaped curve, between the mean and +, – three standard deviations, 99.72% of the observations occur. If the instructor wants to put the exam scores on the normal curve he/she will have to modify the scores for all the students in a way that 50% students will fall below the mean and 50% students will fall above the mean.
Statistically, normal distribution or normal curve can be used for better representation which can help the instructor analyze and adjust the scores if necessary. It also helps instructor assess the students relative to their peers rather than just an individual. However, for data given in this example, the statistically sound method of curving will be a skewed curve. Even though it is advisable to use normal curve method for the grading; modifying data to fit the normal curve may not be appropriate presentation of the data. So, in my opinion, it is best suitable to keep the scores as it is in this example and present the data with a skewed curve.
(Source- allpsych website)
To understand this example better I would like to know if any of you have more ideas regarding method of curving that can be used. Is there any better way to fit this data in normal curve distribution?
Just for fun,