Is the $standarddeviation$ considered a resistant measure of spread in statistics?

• A. The $standarddeviation$ is always zero for any data set.
• B. The $standarddeviation$ is only resistant when the data are symmetric.
• C. Yes, the $standarddeviation$ is resistant and not affected by extreme values.
• D. No, the $standarddeviation$ is not resistant because it is greatly affected by outliers.

Answer: (D)

Verified step by step guidance

1. Understand the concept of a resistant measure of spread: A resistant measure is one that is not significantly affected by extreme values or outliers in the data set.
2. Recall the definition of standard deviation: It measures the average distance of data points from the mean, calculated using the formula \(\sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2}\), where \(x_i\) are data points and \(\bar{x}\) is the mean.
3. Recognize that because standard deviation uses the mean and squares the deviations, extreme values (outliers) have a large impact on its value, increasing the spread measure significantly.
4. Compare this to resistant measures like the interquartile range (IQR), which rely on medians and quartiles and are less influenced by outliers.
5. Conclude that the standard deviation is not a resistant measure of spread because it is sensitive to extreme values and outliers.