Which measure of central tendency is altered by extreme values in a dataset?

Which measure of central tendency is altered by extreme values in a dataset?

• A. Mode
• B. Median
• C. Mean
• D. Range

Answer: (C)

The mean is a measure of central tendency that is significantly affected by extreme values, also known as outliers, in a dataset. This is because the mean is calculated by summing all the values in the dataset and dividing by the number of values. When an extreme value is present, it can drastically increase or decrease the total, thereby skewing the mean. For example, in the dataset {2, 3, 4, 5, 100}, the mean would be (2 + 3 + 4 + 5 + 100) / 5 = 22.8, which does not accurately represent the center of the data if one is considering the majority of values. In contrast, both the mode and median are less sensitive to extreme values. The mode, being the most frequently occurring value, remains unaffected by how large or small other values are. Similarly, the median, which represents the middle value when the data is ordered, only changes if the extreme value falls close to or disrupts the middle of the dataset, making it a more robust measure in the presence of outliers. The range, while it does measure the spread of the data, does not serve as a measure of central tendency and thus isn't directly applicable

The mean is a measure of central tendency that is significantly affected by extreme values, also known as outliers, in a dataset. This is because the mean is calculated by summing all the values in the dataset and dividing by the number of values. When an extreme value is present, it can drastically increase or decrease the total, thereby skewing the mean.

For example, in the dataset {2, 3, 4, 5, 100}, the mean would be (2 + 3 + 4 + 5 + 100) / 5 = 22.8, which does not accurately represent the center of the data if one is considering the majority of values. In contrast, both the mode and median are less sensitive to extreme values. The mode, being the most frequently occurring value, remains unaffected by how large or small other values are. Similarly, the median, which represents the middle value when the data is ordered, only changes if the extreme value falls close to or disrupts the middle of the dataset, making it a more robust measure in the presence of outliers.

The range, while it does measure the spread of the data, does not serve as a measure of central tendency and thus isn't directly applicable