Which dispersion measure is half the distance between the first and third quartiles?

Which dispersion measure is half the distance between the first and third quartiles?

• A. Semi-interquartile range
• B. Range
• C. Standard deviation
• D. Variance

Answer: (A)

The measure described is the semi-interquartile range. The distance between the first and third quartiles is the interquartile range (IQR), which represents the spread of the middle 50% of the data. Taking half of that distance gives the semi-interquartile range (also called the quartile deviation), a dispersion measure centered on the median that reflects typical spread within the central portion of the data. It’s less influenced by extreme values than the full range. The other options don’t tie to quartile spread: the range uses the extreme values (max minus min), while standard deviation and variance describe spread around the mean and incorporate all data points.

The measure described is the semi-interquartile range. The distance between the first and third quartiles is the interquartile range (IQR), which represents the spread of the middle 50% of the data. Taking half of that distance gives the semi-interquartile range (also called the quartile deviation), a dispersion measure centered on the median that reflects typical spread within the central portion of the data. It’s less influenced by extreme values than the full range. The other options don’t tie to quartile spread: the range uses the extreme values (max minus min), while standard deviation and variance describe spread around the mean and incorporate all data points.