Statistics anxiety scores: 8, 45, 16, 18, 30, 4, 18, 42, 43, 45
(Interpretation: 0 – 20 = less anxious; 21 – 30 = moderately anxious; 31 – 50 = severely anxious)
Mean is usually referred to as the computation average of a set of given numbers. It is usually calculated by adding up the scores and dividing the total by the number of scores ( Jones, 2014) . In the set above: 8, 45,16, 18, 30, 4, 18, 42, 43, 45; the mean is calculated in the following manner:
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8+45+16+18+30+4+18+42+43+45=269
269/10=26.9; Thus, the mean in the above distribution is 26.9
On the other hand, median refers to the middle score of a distribution of numbers. The first step of calculating median involves arranging the numbers in numerical order from the smallest to the largest. Then, if the number of scores is an odd number, divide by two and round up to get the position of the median number. However, if the total number of scores is an even number, divide by two. Pick the number in that position and average it with the number in the higher position to attain the median (Weaver, Morales, Dunn, Weaver & Godde, 2017).
Thus, for the set of numbers given above the total number of scores is an even number; thus, the median will be calculated as follows. First, arrange the numbers in numerical order, which is4, 8, 16, 18, 18, 30, 42, 43, 45, and 45. Then, since there is no middle score, one should take the average of the middle two scores, calculating their mean. Remember, that mean is calculated by adding the scores together and then dividing what you get by the number of scores you added. Therefore, in this case the mean will be 18+30, which equals to 48. Then divide 48 by 2, the total number of scores you added. This will result to 24. Hence, the median for the distribution is 24.
Finally, mode refers to the most frequently occurring number in a set of numbers. In the set: 4, 8, 16, 18, 18, 30, 42, 43, 45, 45 there are two sets of mode, which are 18 and 45, since they both occur twice. This set is referred to as a bi-modal distribution ( Heiman, 2013) .
In conclusion, from the three measures of central tendency, median best represents the data. The reason being is that the data of the statistics anxiety scores is an ordinal type of data. This means that the data is in scale form since the results are divided into three, that is, less anxious, moderately anxious, and severely anxious, in order to ease the ranking of students. Median is best used to represent ordinal values of data. Further, the distribution of data is skewed and in strongly skewed sets of data, median is usually preferred to mean.
References
Weaver, K. F., Morales, V., Dunn, S. L., Weaver, P. &Godde, K. (2017). An Introduction to Statistical Analysis in Research: With Applications in the Biological and Life Sciences.Hoboken: John Wiley & Sons.
Heiman, G. (2013). Basic Statistics for the Behavioral Sciences.Boston: Cengage Learning.
Jones, B. (2014). Communicating Data with Tableau: Designing, Developing, and Delivering Data Visualizations.Sebastopol: O'Reilly Media, Inc.
