60. 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?
Answer: B
The median should be used to determine the amount of a typical donation.
The median is a robust statistic that is less influenced by outliers and skewed data, making it the most appropriate choice to represent a typical donation amount in this context.
A) Z-score
The Z-score measures the number of standard deviations a data point is from the mean. While it can help identify outliers, it does not provide a direct measure of a typical donation amount and is sensitive to skewed data.
B) Median
The median is the middle value in a data set when organized in ascending or descending order. It is particularly effective in situations where the data may be skewed or have outliers, as it accurately reflects the center of the data without being disproportionately affected by extreme values.
C) Mean
The mean is the average of all donation amounts and can be heavily influenced by outliers. In cases where donations vary widely, the mean may not accurately represent a typical donation as it can be skewed by particularly large or small contributions.
D) Mode
The mode is the value that appears most frequently in a data set. While it can indicate the most common donation amount, it does not provide a measure of central tendency when data is skewed or when there are many unique donation amounts, making it less reliable in this context.
Conclusion
The median is the most suitable statistic for determining a typical donation amount in this scenario as it effectively mitigates the influence of outliers and skewed data. In contrast, the mean can be distorted by extreme values, the mode may not reflect the overall distribution, and the Z-score is not a measure of central tendency. Thus, the median stands out as the best choice.