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 data set, making it a robust measure of central tendency that remains stable even when extreme values or skewed distributions are present. This characteristic makes it particularly useful for representing typical donations in fundraising scenarios.
The mean, or average, is calculated by summing all values and dividing by the total number of values. This statistic is highly sensitive to outliers; a few extraordinarily high or low donations can significantly distort the mean, leading to an unreliable representation of a typical donation amount.
The median is the value that separates the higher half from the lower half of a data set. Because it only considers the middle value(s), it is not influenced by extreme values, making it the best choice for determining a typical donation amount in the presence of outliers or skewed data.
A z-score indicates how many standard deviations a particular value is from the mean. While useful for identifying outliers, it does not provide a measure of central tendency. Therefore, it does not help in determining a typical donation amount, as it focuses on individual data points rather than summarizing the data set.
The mode is the most frequently occurring value in a data set. While it provides insight into the most common donation amount, it can be misleading when donations are varied or when there are multiple modes. Thus, it does not effectively capture the central tendency in the presence of skewed distributions or outliers.
In evaluating the typical donation amount for a fundraiser, the median is the most reliable statistic, as it is not skewed by outliers or extreme values. The mean is susceptible to distortion from atypical donations, while the z-score and mode do not effectively summarize central tendency. By using the median, the organization can gain a clearer understanding of the typical contributions received.
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