article · African Journal of Advances in Science and Technology Research
This study evaluates measures of central tendency and dispersion using simulated data from four-point and five-point Likert scales across four statements. The statistical metrics examined include the mean, median, mode, variance, and standard deviation, alongside graphical representations. In the five-point scale analysis, the second statement yielded the highest standard deviation at 1.53 and the lowest mean at 2.35, indicating a wide spread of respondent opinions. Conversely, the first statement on the four-point scale produced a bimodal distribution with equal ties of twenty responses between strong agreement and agreement, making interpretation more difficult because the population divides into two distinct groups. Based on the findings, the five-point Likert scale is recommended because it accommodates undecided respondents. Additionally, the standard deviation is highlighted as the preferred metric for interpreting response dispersion around the mean.
Surveys and opinion gathering are essential for understanding public perspectives on critical issues. Selecting the appropriate scale and statistical measures ensures that survey results reflect public sentiment accurately, avoiding misleading conclusions caused by rigid response options or overlooked variations in opinion spread.
This methodological research could inform survey design and data analysis protocols used by market research organisations, polling agencies, and social science practitioners. Because the work is based on simulated data rather than applied testing in an operational setting, it represents an early-stage methodological recommendation that requires real-world deployment and validation.
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This research aims to analyzing measures of central tendency (mean, median, and mode), and measures of dispersion (variance and standard deviation) and to graphically present the simulated data using Likert scale measurement. Mean (μ), Median (Md), Mode (Mod), Variance ( ), and Standard deviation (σ) have been calculated on simulated data using 5 and 4 points Likert scales with four different statements. Data analysis is key in any development especially when there is need to understanding people's opinions on a particular issue that has attracted the attention of a specific population. Likert scale of measurement is one of the methods that use statement problems in collecting statistical data in which the respondent agrees with the opinion or disagrees. Considering the 5-point Likert scale, the measure of dispersion in which statement two had the highest standard deviation of 1.53 and the mean value of 2.35 being the least of the mean values implies the significant spread of the data across opinions. Statement one of the 4-points Likert scale has two modes (bimodal) where the opinions “Strongly Agree” and “Agree” have ties of 20 responses each. This implies that interpretation of such data may be difficult, because the data can be roughly split into two different groups, and can be useful for further research to find a mode to draw conclusions. The best form of Likert scale can be recommended for 5-point Likert scale so as to give room for undecided opinion. Other measures of central tendency and dispersion can be useful in interpretation but the recommended statistical tool is standard deviation as it shows the spread of the opinions about the mean.
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DOI: 10.62154/ajastr.2024.016.010379
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