Correct option is Option B: The standard deviation is a better measure of spread for movies than it is for basketball games.
Visual analysis for movies:
Movies data is more centric to mean and not skewed on a particular side.
Visual analysis for Basketball games:
Basketball games data is not centric to mean but is skewed or say more dense in right then left.
Property of standard deviation and its limitation:
Standard deviation just measures the deviation or spread with respect to mean of collected data. It is non- sensible for skewness of the data and thus more information is needed in such case.
Property of IQR and its limitation:
IQR is interquartile range. IQR generally is less powerful than standard deviation, but more powerful if the data is skewed and its variability has to be measured. It measures the range or say difference between [tex]Q_3 \: and \: Q_1[/tex]
In the movies data, the data is more collected and barely visible to be skewed. Thus standard deviation is best suited for this dataset.
In the basketball data, the standard deviation will fail to give good information about the data. The IQR, is better here since we've to measure variability or dispersion of data which is skewed.
Thus, option B: The standard deviation is a better measure of spread for movies than it is for basketball games; is correct option.
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