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I will never get tired of reminding my readers that the most important assessment is the school-based one, otherwise known as formative assessment, conducted by the classroom teacher. It is not only critical to score and discuss the test outcomes with the class, but also to analyse the test scores and understand what it tells you.
Classroom assessment can be conducted using different formats and instruments. It should never be limited to using written tests because learners learn in different ways as such assessment should be tied to their learning styles. Thus, in computing end of term scores for reporting, it should incorporate all scores obtained using other formats of assessment, such as practical’s, performance to give a true reflection of what the learner knows and can do.
Although analysis of examination is important, it provides the least information to the teacher and school for improvement because the results are reported as grades.
Irrespective of the assessment format used, the extent to which the learner possesses the knowledge, skill or attitude can be quantified. It is this quantification which enables us to carry out the analysis. Such analysis includes the mean, median and mode, which are collectively called the central tendency of a test. The central tendency measure results in a single number that represents the center or middle of a set of test scores.
The mean is the average score of the class. A high mean indicates that generally, learners have mastered the subject content. In classroom assessment, it is for all learners to master the content. The mean is considered the best measure of the central tendency. However, it is affected by outliers (those scores at the extreme ends) which might significantly increase or decrease it since all test scores are used in its calculation. In such situations, the median is the appropriate central tendency to use. The median is the middle score in the class scores arranged from lowest to highest; as such it is a positional average.
When dealing with categorical data, such as gender, colour, breed, the mode is the best choice to compute. The mode is the most appearing score in a set of test scores. Sometimes the test scores may contain multiple modes and in some cases, it may not contain any mode at all. Like the median, it is not affected by extreme scores.
The mean, mode and median are exactly the same in an evenly spread across the spectrum from the lowest to the highest. However, the three main measures of central tendency are best used in combination with each other because they have complementary strengths and limitations.
It is also important to determine how test scores are spread. This is called dispersion. The three commonly analysed measures of dispersion are the range, quartile and standard deviation. The range is the difference between the highest and the lowest score. The higher the value of the range, the higher the spread in data, which is not desirable. The standard deviation measures the distance of each mark from the class mean. The closer the marks to the mean the better because it tells you that learners understanding of the topic is almost the same.
On the other hand, quartiles are the values that divide a list of numerical data into three quarters. The quartile is achieved by ordering data from smallest to largest and divide it into four equal sections. While the median breaks the data into two sections, the quartile divides it into four. Quartiles help calculate the interquartile range which is the range between the first and third quartiles.
Generally, measures of dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct test scores may have the same mean or median, but completely different levels of dispersion (range, standard deviation and quartile), or vice versa.
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