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 represents the middle value in a dataset when arranged in ascending order, making it a robust measure of central tendency that remains stable even when extreme values are present. This characteristic allows it to effectively represent a typical donation amount, especially in cases where the data may be skewed or contain outliers.
The mode is the value that appears most frequently in a dataset. While it can provide insight into common donation amounts, it may not accurately reflect a typical donation if the most frequent donation is significantly lower or higher than the rest, especially in datasets with outliers or skewed distributions.
A Z-score measures how many standard deviations a data point is from the mean, but it does not directly indicate a typical value of a dataset. Instead, it serves as a tool to identify outliers rather than summarize the overall distribution, making it unsuitable for determining a typical donation amount.
The mean is calculated by summing all values and dividing by the number of observations. However, this average is highly sensitive to extreme values, which can skew the representation of a typical donation amount. In cases where donations vary widely, the mean may not accurately reflect the central tendency, unlike the median.
To accurately determine a typical donation amount from potentially skewed data or datasets with outliers, the median is the most reliable statistic to use. It effectively captures the central value of a dataset without being distorted by extreme values, unlike the mean, mode, or Z-score. Therefore, selecting the median ensures a more accurate representation of typical donations.
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