1. **Problem statement:** We want to determine which statistical measures will be equal to zero if all values in a data set are the same. 2. **Key concept:** - If all values are the same, the range, which is max minus min, is zero because max = min. - Variance measures the average squared deviation from the mean. If all values are identical, each deviation is zero, so variance is zero. - Standard deviation is the square root of variance, so it will also be zero. - Interquartile range (IQR) measures the spread between the 75th and 25th percentiles. If all values are the same, IQR is zero. - Mean, median, and mode are measures of central tendency and will be equal to the constant value, not zero unless the common value itself is zero. 3. **Check options:** - A: range, variance, standard deviation, and interquartile range — all zero as explained. - B: mean (usually not zero unless all data are zero), variance, standard deviation, and IQR — mean is not necessarily zero. - C: median (not zero), range, variance, and standard deviation — median not zero unless value is zero. - D: mean, range, variance, and standard deviation — mean not zero. - E: mean, median, mode, variance, and standard deviation — measures of central tendency generally not zero. 4. **Conclusion:** The correct answer is A because all these measures (range, variance, standard deviation, and IQR) will be equal to zero when all data values are equal.