In the statistical analysis, the data is essential in its interpretation and understanding. The weighted mean is a specific mean type that is statistically calculated by the product of weight or probability linked to an assessment, event, or outcome with the quantitative results and concluding by adding up all products. Weight varies since some data arithmetic contributes more "weight" than others. Professors and teachers often prefer the weighted mean in grading the students for the final ranking position.
Rule on How to Calculated Weighted Mean
In the weighted mean calculation, the procedure has to be procedural and progressively advancing to the ultimate solution (Dybach, 2019). Step one list the numbers and the weight in a tabular form not necessarily in tabular form but for easy calculation. Step 2, Multiply every number with the proportional weight assigned to the number. In Step 3, add the values obtained in the 2nd step. Step 4 finds the sum of the weights (Kang et al., 2019). Finally, step 5 divides the total numbers obtained in the previous step by the sum of the weights obtained in step 4.
Detaille Example Illustrating A Weighted Mean.
Assessment Weights Joel scores Joel class grade Martin scores Martin class grade Kirui score Kirui class grade
homework 10 4% 50% 2 20% 0.8 30% 1.2
assignment 20 8% 40% 3.2 50% 4 40% 3.2
Test 1 40 16% 55% 8.8 30% 4.8 50% 8
midterm 40 16% 60% 9.6 50% 8 40% 6.4
Test 3 50 20% 80% 16 70% 14 50% 10
Final exam 70 28% 50% 14 55% 15.4 60% 16.8
Project proposal 20 8% 40% 3.2 60% 4.8 40% 3.2
Total = 250 Total 56.8 Total 51.8 Total 48.8
Advantage of Weighted Average
The weighted average is more accurate than the simple average .it assigns all the values in the data to set a unique weight (Dybach, 2019). In other simple average or the arithmetic mean, all values are treated equally and assigned equal weights, which tend to be biased. In weighted average, the assigned identical weight is more advance in relative importance and accuracy. The weighted average takes into account the relative frequency importance (Kang et al., 2019).
A weighted average is a clear and accessible way in the analysis. It takes consideration of frequency. It is more accurate than the arithmetic mean. The weighted mean is unbiased in deciding on the mean. The weighted mean is a necessary tool to learn in statistics as it helps in presenting data in a precise formal way.
Dybach, I. (2019). undefined. Economics of Development, 18(1), 33-43. https://doi.org/10.21511/ed.18(1).2019.04
Kang, K., Absher, R., Farrington, E., Ackley, R., & So, T. (2019). Evaluation of different methods used to calculate ideal body weight in the pediatric population. The Journal of Pediatric Pharmacology and Therapeutics, 24(5), 421-430. https://doi.org/10.5863/1551-6776-24.5.421
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