MYP Extended Mathematics Measures of Spread Questionbank

On a box-and-whisker plot, if the central box is very narrow (representing a small interquartile range) compared to the total length of the whiskers (representing a large range), what does this specifically indicate about the data distribution?

In Data Set ${A}$, the population standard deviation is small (${ ext{\sigma} = 2 }$), while in Data Set ${B}$, it is large (${ ext{\sigma} = 10 }$). If both sets share a mean of , in which set is the mean a more representative "typical" value?

A researcher is studying minimum overnight temperatures to assess the risk of frost damaging crops. Why might they prioritize the range over the interquartile range (IQR) for this study?

True or False: Because the range depends entirely on the maximum and minimum values, it is highly sensitive to outliers and can misrepresent the variability of the majority of the data set.

A population has a mean $\mu$ and a standard deviation $\sigma > 0$. If an additional data point is added to the population that is exactly equal to the mean $\mu$, what happens to the population standard deviation?