Final answer:
The statement that the IQR always shows a good measure of observations is false, as its effectiveness can vary based on the data's distribution, skewness, and presence of outliers.
Step-by-step explanation:
The statement 'The IQR always shows a good measure of observations' is false. The Interquartile Range (IQR) is indeed a measure of statistical dispersion, representing the range between the first and third quartiles (the middle 50% of the data). While it provides a good measure for the spread of the middle 50% of data in many cases, especially for symmetrical distributions, it may not be as useful for skewed distributions or when there are significant outliers. In such cases, other measures might better represent the variability of the data, such as using a combination of variance and standard deviation.
For example, if you have a dataset with a significant skew or outliers, the IQR might not capture the extent of variability effectively. Additionally, if the dataset has a bimodal distribution, or if there's a significant gap within the IQR range itself, this can also make the IQR less representative of the data's overall spread.