A nonprofit organization ran a fundraiser and would like to determine the amount of a typical donation. Which statistic is less affected by outliers and skewed data and should be used to determine the amount of a typical donation?
Median is less affected by outliers and skewed data.
The median is the middle value in a dataset when ordered, making it robust against extreme values or skewed distributions. This characteristic enables it to accurately represent a typical donation amount even when the dataset contains outliers or is not symmetrically distributed.
Z-scores measure the number of standard deviations a data point is from the mean. While they provide insight into the relative position of values, they are highly sensitive to outliers. A single extreme donation can significantly affect the mean and thus distort the interpretation of other donations when calculating Z-scores.
The mean is calculated by summing all donation amounts and dividing by the total number of donations. It is greatly influenced by outliers; for instance, a few large donations can raise the mean significantly, making it an unreliable indicator of a typical donation when the dataset is skewed.
The mode represents the most frequently occurring value in a dataset. While it can indicate the most common donation amount, it does not provide a central tendency measure that reflects the overall distribution, especially if the dataset contains many unique donation amounts or is skewed.
In summary, the median is the best choice for determining a typical donation amount in the presence of outliers and skewed data. Unlike the mean, which can be distorted by extreme values, and the Z-score, which is sensitive to outliers, the median provides a stable measure of central tendency. The mode, although useful for identifying common values, does not convey the central distribution of the data effectively. Thus, for accurate representation in this scenario, the median is the most appropriate statistic to use.
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