Which statistic represents the range of the middle 50% of an ordered data set?

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Multiple Choice

Which statistic represents the range of the middle 50% of an ordered data set?

Explanation:
The interquartile range measures the spread of the middle 50% of an ordered data set. It’s found by subtracting the first quartile from the third quartile (IQR = Q3 − Q1). Q1 marks the 25th percentile and Q3 the 75th percentile, so the distance between them covers the central half of the data. This statistic highlights dispersion while being less affected by outliers than the overall range. In a boxplot, the box height is the IQR, reflecting the middle half’s spread. The range includes the extreme values from minimum to maximum, and variance or standard deviation reflect spread around the mean for the whole data set, not specifically the central 50%. For example, if Q1 is 10 and Q3 is 30, the IQR is 20.

The interquartile range measures the spread of the middle 50% of an ordered data set. It’s found by subtracting the first quartile from the third quartile (IQR = Q3 − Q1). Q1 marks the 25th percentile and Q3 the 75th percentile, so the distance between them covers the central half of the data. This statistic highlights dispersion while being less affected by outliers than the overall range. In a boxplot, the box height is the IQR, reflecting the middle half’s spread. The range includes the extreme values from minimum to maximum, and variance or standard deviation reflect spread around the mean for the whole data set, not specifically the central 50%. For example, if Q1 is 10 and Q3 is 30, the IQR is 20.

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