Interpretation
Table 1 and Table 2 in Appendix present the central tendency measures, which are mean, median, and mode, for regular homework hours and homework hours during finals, respectively. According to Table 1, the average (mean) of the data is 6.33, the median is 6.00, and the mode (most frequent value) is 5. In this data, several modes were present, but the smallest was chosen. According to Table 2, the mean was 16.70, the median was 17.00, and the most recurring value was 20.
Discussion
The mean of a dataset is the sum of all entries divided by the total number of entries. The mean is one of the most common measures of central tendency used to show the average tendency or the center of a dataset (Salvatore, 2021). For instance, from Table 1, most of the regular homework hours are centered at 6.33, and for Table 2, they are centered at 16.70. Median, on the other hand, is the value that falls exactly at the center when data are ordered from smallest to largest (Cao, 2021). It is used to partition the data into two to specify the central position in the data. The central positions in Table 1 (regular homework hours) are 6 and 17; in Table 2 (homework hours during finals), they are 6 and 17.
The other central tendency, called mode, represents the most frequently entered value in the dataset. Mode helps identify the most common value among the entries (Cao, 2021). For example, Table 1 shows that the most popular regular homework hours are five. In Table 2, the most popular homework hours during finals are 20. It can also be used to detect peaks, mainly when the data contains many of them. This statistical measure applies to nominal data with categories and identifies the most common category. To compute this, the dataset is sorted categorically or numerically, and the response that occurs more regularly is selected.
Comparison
The three measures of central tendency have distinct strengths and weaknesses that determine their application. The mean applies only to ratio and interval data because it requires equal spacing between values or scores. That means the data should be symmetrically distributed with no extreme outliers (Salvatore, 2021). Outliers are values that are significantly distant or extreme in a dataset. The median, however, is not affected by outliers or data that is scattered on the extremes. It is primarily applicable to non-normally distributed data or skewed data. The median can also be used with ratio, interval, and ordinal data.
On the other hand, mode is mainly applied in discrete or categorical data where distinct entries occur more frequently than others. When deciding the best measurement of central tendency, it is essential to consider the dataset’s distribution (Chakrabarty, 2020). In normally distributed or symmetric data, all the measures of central tendency are often equal. Therefore, these tendencies can complement each other in symmetric datasets. For instance, in Table 1, the tendencies are equal, as seen in Table 2. However, in skewed datasets, the median is more appropriate because extreme values do not affect it.
References
Cao, W. (2021). Discussion on mean, median, mode and its validity and table number. Journal of Contemporary Educational Research, 5(3).
Chakrabarty, D. (2020). Some properties of measure of central tendency of data.
Salvatore, D. (2021). Theory and problems of statistics and econometrics (2nd Ed.). McGraw-Hill.
Appendix
Table 1. Regular Homework Hours
Table 2. Homework Hours During Finals