The box plots below show attendance at a local movie theater and high school basketball games:Which of the following best describes how to measure the spread of the data? (1 point)The IQR is a better measure of spread for movies than it is for basketball games.The standard deviation is a better measure of spread for movies than it is for basketball games.The IQR is the best measurement of spread for games and movies.The standard deviation is the best measurement of spread for games and movies.
Question
The box plots below show attendance at a local movie theater and high school basketball games:Which of the following best describes how to measure the spread of the data? (1 point)The IQR is a better measure of spread for movies than it is for basketball games.The standard deviation is a better measure of spread for movies than it is for basketball games.The IQR is the best measurement of spread for games and movies.The standard deviation is the best measurement of spread for games and movies.
Solution
To answer this question, we first need to understand what the terms IQR (Interquartile Range) and standard deviation mean in terms of data spread.
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IQR: This is a measure of statistical dispersion, or in simpler terms, it's a measure of where the "middle half" is in a data set. It's calculated by subtracting the first quartile (25th percentile) from the third quartile (75th percentile).
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Standard Deviation: This is a measure that is used to quantify the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Now, coming back to the question, whether IQR or standard deviation is a better measure of spread for movies or basketball games depends on the data distribution.
If the data is normally distributed (i.e., it follows a bell curve), then the standard deviation would be a good measure of spread. This is because it takes into account all data points, including outliers.
On the other hand, if the data is skewed (i.e., it does not follow a bell curve), then the IQR would be a better measure of spread. This is because it only considers the middle 50% of the data and is not affected by outliers.
Without the actual box plots or additional information about the distribution of the data, it's impossible to definitively say which measure is better for the given scenarios.
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The Interquartile Range (IQR), a fundamental measure in Descriptive Statistics, is best described as: A. The difference between the highest and lowest values in a dataset. B. The variance between the mean and the median of a dataset. C. The gap between the upper (Q3) and lower quartile (Q1) of a dataset. D. The summation of the dataset's upper (Q3) and lower quartile (Q1).
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