Question

Which is more affected by extreme observations, the mean or median? And how about the standard deviation or IQR?
mean, standard deviation
mean, IQR
median, IQR

Answer 1

Extreme observations (outliers) have a more significant effect on the mean and the standard deviation than on the median and the interquartile range (IQR).

- **Mean**: The mean is sensitive to extreme values because it takes all data points into account. An extremely high or low value can skew the mean significantly.

- **Standard Deviation**: The standard deviation also takes all data points into account and is affected by extreme values, as it measures the spread of the data around the mean.

- **Median**: The median, which is the middle value when the data is ordered, is less affected by outliers. It remains stable regardless of extreme values unless they change the overall ordering of the data.

- **IQR**: The interquartile range (IQR), which measures the spread of the middle 50% of the data, is also resistant to outliers since it focuses on the values between the first quartile (Q1) and the third quartile (Q3) and ignores the extremes.

Based on this information, the answer would be:

**mean, standard deviation** are more affected by extreme observations compared to **median, IQR**.