Statistics can be misleading due to the statistician’s interpretation of data and which figures are highlighted. Measures of central tendency, such as mean, median, and mode, can also be misleading. Questions asked in surveys and the representativeness of the sample can also affect the accuracy of statistics. Numbers and statistics cannot represent the individual.
There’s an old adage that numbers don’t lie, but liars know how to tell. In a way this represents people’s distrust of statistics. Statistical interpretation can make data appear misleading. It depends on the statistician’s interpretation of the data and which figures are brought up as key points in a statistical report.
For example, in classical high school, students now study measures of central tendency, which are mean, median, mode, and range. The mean is a sum of all data points, divided by the number of data points. For example, you could add up a person’s test scores and divide it by the number of tests to determine a grade. However, the mean can be affected by what’s called an outlier, a number far outside the normal testing range. This may suggest that averaging can be a misleading way of evaluating performance.
If a person does five tests perfectly and fails a sixth test thus earning a zero, the average reflects this. If the tests are all worth 100 points, for example, the average score is about 85%. However, this doesn’t really suggest average performance in this case due to the zero outlier.
Another measure of central tendency that can be used is the estimate of the median. The median is the middle number in a group of numerically arranged data. If a statistician evaluates for the median, it may not be representative of a true performance average or whatever is being evaluated. The median cannot account for a range of data which can be huge and therefore can be misleading.
Central tendency assessed by mode simply means looking at a number that occurs most often in a dataset. So the test taker, for example, has a modality of 100. However, this does not reflect that the person taking the test failed to take one, which is misleading.
Other ways statistics can be misleading are how questions are asked, perhaps in a survey, and the degree to which the survey is a representative sample of a community. If you survey a group of high school students and ask, “How satisfied are you with your education on a scale of 1 to 5?” very different answers can be obtained depending on whether the group is representative of the “average” student.
If you’re looking at a group of students who all get As and go to a great, well-funded school, publishing that data as a representative sample is deliberately misleading. If you ask students from different schools with different grades, a survey is likely to be more representative and fairer. However, if you ask students what they think about schools and then publish the results as a representative sample of the general population, the answers will be highly skewed.
Numbers can seem very factual and some are misled by numbers simply because they look like fact and have indisputable value. Therefore, statistical data can often be used in a misleading way to fool people with numbers and make controversial things seem more like reality. Reputable statisticians know that questions must be generalized and must also be asked of people representing populations.
However, numbers and statistics can be misleading because they do not represent the individual. They can show how people ‘in general’ respond to an idea, product or political candidate. They cannot show how a single person will feel in all his infinitely variable qualities.
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