Which of the following is the semi- interquartile range of a distribution?
Answer Details
The semi-interquartile range of a distribution is the measure of dispersion or spread of data around the median. It is half of the difference between the upper quartile and the lower quartile. Therefore, the correct answer is \(\frac{1}{2}(\text{Upper quartile - Lower quartile})\).
To find the interquartile range (IQR), we subtract the lower quartile (Q1) from the upper quartile (Q3), i.e., IQR = Q3 - Q1. Then, the semi-interquartile range (SIQR) is half of the IQR, i.e., SIQR = (Q3 - Q1) / 2.
The other options listed in the question are not measures of dispersion or spread around the median, so they are not correct answers to the question.