Describe the different ways in which the mean, median, and mode contribute to the interpretation of data. Be specific. Give an example in which these numerical descriptors of data can be effective (e.g., test scores).
One example in which the mean, median, and mode can be used effectively to reduce groups of data and illustrate measures of central tendency and variability is in a distribution of test scores.
Measures of central trendency are used to establish trends and make predictions based on results. Estimates are established and provide indicators.
The mean is the accumulation of all scores divided by the number of scores - such as when finding an average for a school report card:
52%; 75%; 60%; 81%; 52%; 65%; 64%
The mean would be the total of 449 divided by 7 (number of scores) = 64% (rounded off)
By comparison, the median is the middle score. Care must be taken to arrange the data in order, such that we get:
52%; 52%; 60%; 64%; 65%; 75%; 81%
Therefore the median is also 64%. This reinforces the mean score. In this case, they are the same. Unfortunately, some information is lost in both these instances as the score of 81% and that of 75% appear to be overlooked.
The mode is the most frequently occuring score. In this case that would be 52%.
By comparison, in this instance, the mode would be a poor indicator of the learners results and would be an unfair measure when discussing theis learners' results.
Schools (such as this example) need to use measures of central tendency to establish patterns, understand strengths and weaknesses that the patterns reveal in some subjects and to place learners in categories that suit their abilities.
Say, for example, the score of 52% was for English and there are many learners with 52%, then the mode would be a good measure and show that the school needs to work on their English scores.
Say, most children scored over 80% for Maths, the mean would show a high score and the school would know that they need to maintain these results. The median would have to be assessed in relation to the other scores to ensure that , as the middle data point, it is reflective of most scores in the range.
Hence, it is apparent that all mesures of central tendency (there is also the Standard Deviation) serve an important function but as statistical tools they must be considered within their context.