To determine which measure of variability best represents the shape of the distribution from the boxplot described, we need to analyze both the range and the interquartile range (IQR).
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Range: The range is the difference between the maximum and minimum values of the data set. In this case, the range extends from 2 to 9.5, which indicates that there are some low values (at 2) and high values (at 9.5) present. However, since the maximum value is not close to the middle of the distribution, it suggests that the data might be spread out widely, potentially pointing towards skewness.
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IQR: The interquartile range is the difference between the first quartile (Q1) and the third quartile (Q3). In this instance, the first box extends from 4 to 5.5, and the second box from 5.5 to 7. This indicates that most of the data is clustered between 4 and 7. The IQR in this case is \(7 - 4 = 3\). Given that both boxes indicate a concentration of data around the middle values (4 to 7), this suggests that the distribution has a more concentrated core.
Based on the information provided:
- The presence of a longer range on the lower side (2) compared to the higher side (9.5) indicates a right skew in the range.
- However, the IQR showcases that the central 50% of the data is more concentrated and does not exhibit the same spread as the full range.
Since the boxplot exhibits two distinct clusters of data without severe outliers, and the IQR is more representative of the central tendency, the more appropriate measure of variability is the IQR.
The best answer is: IQR, the shape of the distribution is skewed to the right.