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# Misrepresentations and Fallacies in statistics

One area of mathematics called statistics is concerned with gathering, analyzing, and managing data, frequently to make it more understandable and useful. (Brown & Kass, 2009).

Falsehoods and representational distortions, however, may have an impact on how customers and casual observers interpret data. When presenting data, some sleights of hand might be employed to change the meaning for the viewer. (Campbell, 2004).

Additionally, fallacies may affect how individuals perceive represented facts. (Campbell, 2004).

Fallacies are erroneous presumptions that serve as the foundation for mistaken beliefs. This paper will use the graphical statistics provided in the modules notes to find out how fairly the data is presented as well as point out statistical fallacies including misrepresentation. This will be done to illustrate that the meaning of a set of data can be influenced by misrepresentation and fallacies.

## Number of Non-Natural Deaths by Regions Reporting Period July 1, 2004 - June 30 2007

In this reporting period the Americas account for 53% of the non-natural deaths abroad

The data is presented fairly where the number of deaths and the regions are properly given. The conclusion made is also fair. Additionally, dates are also given to distinguish the period of this research with any other times in the history. However, misrepresentations of data are also seen in the graph above. First, the bases for dividing the world into the regions above are not given; continents (Americas, Europe and Africa) are compared with regions of the Asian continent. Therefore, these regions are not clearly defined and it is hard to correctly identify which countries fall into the category of East Asia pacific, Middle East and South Central Asia. Another misrepresentation is in the fact that that the generalization of these regions does not show the spread of non-natural deaths in each region (Cressie, 2015). First, the spatial variation of deaths in each region is not given. Hence, one is not able to compare countries. At the same time, the number of unnatural deaths in each region is not compared with the population as well as the total number of deaths in each region. While the information provided is fair, it could have several meanings if areas pointed out above are not clarified. For this reason, clarification of the above areas and inclusion of additional data is important in creating a clearer meaning.

## 5 Causes of Death over the last Four Reporting Periods

The graph above is fair in representation of the number of deaths caused by various reasons. One wishing to compare deaths caused by vehicle accidents, homicide, Suicide, drowning and terrorists actions can get a clear picture in real figures. Vehicle accidents are also seen to be the leading causes of deaths while terrorist action is the least. However, one of the most important misrepresentations of data in the graph includes lack of the place where the research was conducted. As a result, the reader is not likely to know exactly where the above occurrences were observed. One may even think that it is an explanation of the bar chart in figure 1. One of the fallacies that may influence readers’ interpretation of information this graph is the assumption that all reporting periods represent distinct times. However, the periods represented in this graph are largely overlapping with each beginning 6 months after the preceding 3-year-period. Therefore, evaluation of four distinct periods that largely overlaps makes it hard for the reader to compared and observe the trend. While the data presented on the bar chart may be fair, the comparison is very hard since reporting periods are largely overlapping. At the same time, the graph does not show where the data was collected.

## Percentage of Non-Natural Deaths by Year

Figure 3 above also shows an attempt to fairly represent data. The percentages of non-natural deaths were 35, 37 and 28 in 2004, 2005 and 2006 respectively. The statistician in the above pie chart continues to conclude that the percentages of deaths reduced by close to 10%. However, base-rate fallacy can influence consumers understanding of this conclusion of this data (Bar-Hillel, 1980). First, the pie chart does not give the base that was utilized to calculate these percentages; it is not known if non-natural deaths were compared with the natural deaths, total deaths, every 1000 people or the entire population (Bar-Hillel, 1980). For instance, if the absolute number of non-natural deaths did not change of this period while the entire population increased, the percentage of deaths compared to the general population would be seen to be reducing. At the same time, if the rate of non-natural deaths increased marginally but the rate of natural or total deaths increased at a higher rate, the result seen in the pie charts could be observed if the latter two variables were utilized as the base. In this sense, the conclusion drawn through observation of data presented in the above pie chart constitutes misrepresentation. It is not clear how he/she settled on this conclusion out of many possible conclusions.

## Conclusion

While the field of statistics is created to enhance collection, analysis and presentation of data to make it meaningful, there are a number of factors that influences the meaning of data as perceived by consumer. Tricks described as misrepresentation of data as well as fallacies affects the meaning of data. As seen in the above graphical representation, a set of data can have different meanings according to how it is represented. In some instances, misrepresentations and fallacies makes a set of data to have many meanings. In other instances, it may make data meaningless.

## References

Brown, E. N., & Kass, R. E. (2009). What is statistics?. The American Statistician, 63(2), 105- 110.

Campbell, S. K. (2004). Flaws and fallacies in statistical thinking. Courier Corporation.

Bar-Hillel, M. (1980). The base-rate fallacy in probability judgments. Acta Psychologica, 44(3), 211-233.

Cressie, N. (2015). Statistics for spatial data. John Wiley & Sons.