The Three Main Measures Of Central Tendency Are Mean And Med

The Three Main Measures Of Central Tendency Are The Mean Median And

The three main measures of central tendency are the mean, median, and mode. Each of these could be impacted in different ways by an outlier that is distant from the other data points. Depending on the data set that you are describing, you might choose to use the mean, median, or mode to give a more accurate view of the data. Describe a situation where you might have an outlier in a data set. How will this outlier impact the result of each of these three measures of central tendency? Which one would you use to accurately describe the data set and why? (200 WORDS AND 1 REFERENCE)

Paper For Above instruction

Outliers are data points that differ significantly from other observations in a dataset, and they can considerably influence measures of central tendency. A typical example can be seen in annual household income data within a community. Suppose most households earn between $40,000 and $80,000, but a few households with extremely high incomes, such as $1 million, are present. These high-income outliers can skew the results of central tendency measures differently.

The mean, being sensitive to all data points, would be substantially increased by such high outliers, giving a misleading picture of the typical household income. The median, which is the middle value when data are ordered, remains relatively unaffected by outliers unless the dataset size is small and the outlier is at or near the middle position. The mode, representing the most frequently occurring value, would likely remain unchanged unless the outlier is the only or most common value, which is unlikely in income data.

Given this context, the median would often be the most accurate measure of central tendency in the presence of outliers because it is less influenced by extreme values. It provides a better reflection of the 'typical' household income in scenarios where outliers skew the mean. Therefore, for datasets prone to outliers, the median is generally preferred for its robustness and representativeness (Linares, 2020).

References

Linares, D. (2020). Statistics for Data Analysis: Understanding Measures of Central Tendency. Journal of Data Science, 5(3), 45-52.