Question: Which of the following measures of dispersion is resistant to extreme values?
The following measures of dispersion are resistant to extreme values:
- Quartile deviation: This measure of dispersion is calculated by finding the difference between the third quartile and the first quartile. The third quartile is the median of the upper half of the data set, and the first quartile is the median of the lower half of the data set. Since the quartile deviation is calculated using the medians of the data set, it is not affected by extreme values.
- Interquartile range (IQR): This measure of dispersion is calculated by finding the difference between the third quartile and the first quartile. The IQR is similar to the quartile deviation, but it is more commonly used.
- Median: The median is the middle value of a data set when the data is ordered from least to greatest. The median is not affected by extreme values because it is calculated using the middle value of the data set.
The following measures of dispersion are not resistant to extreme values:
- Range: The range is calculated by finding the difference between the highest and lowest values in a data set. The range is very sensitive to extreme values, so it is not a good measure of dispersion for data sets that contain extreme values.
- Standard deviation: The standard deviation is calculated by finding the average distance between each data point and the mean of the data set. The standard deviation is sensitive to extreme values because it is calculated using the average distance between each data point and the mean.
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