Data collected from any research does not make sense until a statistical analysis is conducted to help draw conclusions. These analysis include measure of central tendency (median, mean, and mode), and the measure of variation (standard deviation, range, and variance). The mathematical analysis of this essay sourced its data from a research conducted to determine the extra hours spend my undergraduate student in a college (not named) to study during weekends (Sage, 2017). The reason I chose the data below is the area of study that the research concentrated on. I have always had the desire to understand the true weight of studying a particular course and learn about the ease or complexity of various college majors. Besides, the simplicity of the figures (small whole numbers) enticed me to choose this data set.
| College Major | Number of hours |
| Economics | 7 |
| Mathematics | 6 |
| Statistics | 6 |
| Literature | 5 |
| Engineering | 9 |
| Management | 5 |
| Computer Science | 8 |
| Sociology | 2 |
| Human Resource | 3 |
| International Relations | 4 |
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Measure of Central Tendency
This is specifically meant to use one number/figure to represent a large set of data.
Mean – This is the arithmetic average for any set of numeric or statistical data. Mean is calculated by adding all numerical values in a data set followed by dividing through using the total count of entities. 5.5 represents the average number of hours spent on weekends by students in various majors in that particular college.
= 5.5
Median – The median score of any dataset is the figure that evenly divided data into half so that the number of scores are equally distributed below and above the median figure. Data is arranged in ascending or descending order to determine the central figure. If two figures appear at the center, they are averaged. Again 5.5 is the median.
2, 3, 4, 5, 5, 6, 6, 7, 8, 9 = = 5.5
Mode – This is the most repetitive figure in the dataset. In our case we have two values; 5 and 6.
Measure of Variation
Variability is the extend by which data in any given datasheet is different (spread out) or clustered (similar).
Range – Range is the difference between the highest figure and the lowest figure in any statistical data. Once these two figures are identified, they are subtracted from one another, based on magnitude. In this case, 7 is the range.
2 , 3, 4, 5, 5, 6, 6, 7, 8, 9; 9 – 2 = 7
Variance – It represents the average of all values deviated from the mean in squared form. It uses the formula:
Where Σ is summation, M is the mean of the dataset, x is individual score, and N is the total number of entities. From the datasheet, the variance is 4.72
| Hours | 6 | 5 | 4 | 6 | 7 | 8 | 3 | 5 | 9 | 2 | Total |
| Deviation from mean (x-M) | 0.5 | 0 | -1.5 | 0.5 | 1.5 | 2.5 | -2.5 | 0 | 3.5 | -3.5 | |
| (x-M) 2 | 0.25 | 0 | 2.25 | 0.25 | 2.25 | 6.25 | 6.25 | 0 | 12.25 | 12.25 | 42.50 |
Applying the formula, = 4.72
Standard Deviation – This is the average value by which figures in statistical data vary about the mean value. It is computed by finding the square root of the variance.
)
4.72 = 2.17
References
Sage, S. (2017). Making Sense of Data: Measure of Central Tendency and Variability . https://us.sagepub.com/sites/default/files/upm-assets/76926_book_item_76926.pdf .
