The mean, median, and mode are frequently referred to as the measures of central tendency. All three of these are used commonly, especially by the media when trying to make a point or persuade an audience to some point of view. However, each of these three statistical measures has their own shortcomings.
For your own original contribution to this Discussion Board, complete the following:
Research the shortcomings of measures of central tendency. Summarize your findings and cite your sources.
Find an example where a mean, median, or mode was used by the media or a company to make a specific point. Evaluate this use and then share your evaluation with the class. Be sure to specifically discuss any caveats or risks associated with the way the organization in your example used their central tendency metric.
Discuss if you think the right measure was used. Share a recommendation for a better measure if you think there is one.
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The measures of central tendency, including the mean, median, and mode, are commonly used in statistics to represent the average or typical value of a dataset. However, these measures have their own shortcomings that can limit their effectiveness in accurately capturing the characteristics of a dataset.
The mean is often used to summarize a dataset, but it can be heavily influenced by extreme values. For example, if a dataset has a few extremely high or low values, the mean may not accurately represent the majority of the data. One source of information on this topic is from the University of California, Los Angeles (UCLA), which states that the mean is sensitive to outliers in the data, making it an inappropriate measure when extreme values are present.
The median, on the other hand, is less affected by extreme values, but it can also be limited in its ability to represent the overall distribution of the data. The median only considers the value in the middle of a sorted dataset, disregarding the rest of the values. The National Institute of Standards and Technology (NIST) highlights that the median may not accurately reflect the spread or shape of the data distribution.
The mode, as the most frequent value, can be useful in identifying the most common category or value in a dataset. However, it may not provide a representative value for datasets with multiple modes or continuous numerical data.
An example where a measure of central tendency was used by the media is in reporting average salaries. The media often reports the mean or median salary of a particular profession or industry to provide information on typical wage levels. However, this use of the measure can be misleading if there is a significant wage disparity within the profession. For instance, if a profession has a few high earners and many low earners, reporting the mean salary could overestimate the average income, while reporting the median salary would provide a more accurate representation of typical income levels.
In this case, the use of the median would be more appropriate due to the potential presence of extreme values that could heavily influence the mean. However, it is worth noting that even the median may not provide a complete picture of wage distribution, particularly in cases where there is a wide range of salaries or significant variations between different regions or job levels.
A better measure to consider could be the percentile, which provides information on the position of a particular value relative to the rest of the dataset. By reporting salary percentiles, such as the median, 25th percentile, or 75th percentile, a more comprehensive understanding of the wage distribution could be obtained, which would provide a clearer representation of the typical income levels within a profession or industry.
In conclusion, while the mean, median, and mode are frequently used measures of central tendency, they have limitations that should be considered when interpreting data. The choice of which measure to use depends on the characteristics of the dataset and the specific purpose of the analysis. In cases where extreme values or variations exist, alternative measures such as percentiles may provide a more accurate depiction of the data.
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