Practise MYP Extended Mathematics questions on 8.1 Measures of Spread and review the explanations to check your understanding.
Use these questions for topic practice and to find ideas you want to revisit in your notes or lessons.
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 , the population standard deviation is small (), while in Data Set , it is large (). 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 and a standard deviation . If an additional data point is added to the population that is exactly equal to the mean , what happens to the population standard deviation?
The middle of the data values are tightly clustered, while the extreme values are widely dispersed.
There are significantly more data points located in the whiskers than in the central box.
The data is uniformly distributed, meaning values are spread evenly across the entire range.
The standard deviation is likely to be zero because the middle of the data is so consistent.
Data Set A, because the values are more tightly clustered around the mean
Data Set B, because the values are more widely scattered
Neither, as the median must be known to judge representativeness
The mean is equally representative in both sets because they have the same mean
The range is easier to graph on a box-and-whisker plot
The range focuses on the extreme minimum temperature, which is critical for determining if frost occurred
The IQR is only valid for symmetric data sets
The IQR ignores the mean, which is necessary for frost prediction
True
False
It decreases
It becomes zero
It remains exactly the same
It increases
