Question

1. a data set of 30 observations has a distribution that is approximately symmetric and unimodal with no outliers. if an outlier that is much larger than all other values is added to the data set, what effect will this have on the standard deviation and the interquartile range?

the standard deviation will increase noticeably, but the interquartile range will remain close to its original value.
both the standard deviation and the interquartile range will greatly increase.
the standard deviation will remain close to its original value, but the interquartile range will increase noticeably.
both the standard deviation and the interquartile range will remain close to their original values.
clear all

Explanation:

The standard deviation is sensitive to outliers as it measures the spread of all data points from the mean. An outlier that is much larger than other values will increase the standard deviation. The interquartile range (IQR), on the other hand, is based on the middle 50% of the data (Q1 - Q3) and is not affected by extreme values (outliers). So when an outlier is added, the standard deviation will increase noticeably, but the inter - quartile range will remain close to its original value.

Answer:

The standard deviation will increase noticeably, but the interquartile range will remain close to its original value.