Question

one way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. the following histograms summarize the distributions of the root-mean-square times for two sources of disturbances. based on the histograms, which of the following correctly compares the two distributions? a the median of the earthquake disturbances is equal to the median of the mining disturbances. b the median of the earthquake disturbances is less than the median of the mining disturbances. c the range of the earthquake disturbances is equal to the range of the mining disturbances. d the range of the earthquake disturbances is less than the range of the mining disturbances. e the mode of the earthquake disturbances is equal to the mode of the mining disturbances.

Explanation:

• For median: Earthquake's data is left - skewed (more low - value bars), mining's is more centered. Earthquake's median (middle value) is lower as its lower - value bins have higher frequency.
• For range: Both have max at 1.6 and min at 0, so ranges are equal. But let's re - check median. Earthquake's peak is at 0 - 0.2, mining's at 0.6 - 0.8. The middle value (median) for earthquake will be in lower bins, so earthquake's median < mining's median.
• Mode: Earthquake's mode bin (0 - 0.2) vs mining's (0.6 - 0.8) – not equal.
• Range: Both min is 0, max is 1.6, so range is 1.6 - 0 = 1.6 for both? Wait, no, wait the x - axis: both go from 0 to 1.6. But the median: Let's think about cumulative frequency. For earthquake, the first bin (0 - 0.2) has high frequency (0.35), then 0.2 - 0.4 (0.20). For mining, 0.4 - 0.6 (0.20), 0.6 - 0.8 (0.35), 0.8 - 1.0 (0.25). The median is the value where 50% of data is below. Earthquake's data is more concentrated on lower end, so its median is less than mining's.

Answer:

B. The median of the earthquake disturbances is less than the median of the mining disturbances.