Basic statistics for ESL teachers

Basic statistics for ESL teachers
1 answers
This short article aims to briefly discuss three important ideas that are often employed in analysing students' examination and test scores: range, mean (average), median. The mean, and the median are two of the measures of location. For the purpose of simplicity and illustration, the following ESL test scores shall be used:Class A: 25%, 37%, 76%, 89%, and 50%; Class B: 27%, 42%, 67%, 89%, and 78%The range is defined as the difference between the highest and the lowest scores. In this case, the range of class A = 89 ─ 25 = 64% and class B = 89 ─ 27 = 62%. As can be seen, both classes have almost the same range. The range gives the novice ESL teacher an idea of the spread between the most extreme scores; however, it does not give any information concerning the other scores. A more useful value is the average.To calculate the average, add the scores and divide the sum by the number of scores: the average for class A = (25+37+76+89+50)÷5 = 55.4% and for class B = (27+42+67+89+78)÷5 = 60.6%. Overall, class B has performed better than class A; however, just looking at the average doesn’t always give you the whole picture. Suppose that class C also had an average of 60.6%: although on average both class B and class C have performed equally well, it does not mean that the students had identical scores, e.g. if class C’s scores were 38, 40, 93, 37, and 95, the average would be 60.6% too. Notice also how a few relatively high scores can lift the average score: in contrast, a few relatively low scores can lower the average score. Because of this, the novice ESL teacher should consider using the median.The median is the middle score in a set of scores arranged in ascending order. The median for class A = 50%, and for class B = 67%. Unlike the mean, the median is not influenced by extreme scores. Where there is an equal number of scores, simply calculate the average of the two middle terms, e.g. the median of 25%, 36%, 46%, 58%, 76%, 80% is (46+58)÷2 = 52%. Finally, don’t forget: when the averages from two or more identical ESL test/examination classes are very close in value, always look at the individual ESL test/examination scores carefully – before coming to any conclusions.   

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