Question

the histogram represents boiling temperatures, in degrees celsius, of tap water and of a saltwater mix.
boiling temperatures
the median boiling temperature of the tap water is 100°c. the median boiling temperature of the salt water is 102°c. which statement about the means is most likely true?
the mean of the tap water boiling temperatures is about 1° greater than the mean of the saltwater boiling temperatures.
the mean of the tap water boiling temperatures is about 4° less than the mean of the saltwater boiling temperatures.

Explanation:

To determine the most likely statement about the means, we analyze the histogram and the given medians. The median of tap water is \(100^\circ\text{C}\) and saltwater is \(102^\circ\text{C}\). From the histogram, the saltwater (purple bars) has more trials at higher temperatures (\(102^\circ\text{C}\), \(103^\circ\text{C}\), \(104^\circ\text{C}\)) compared to tap water (blue bars). This suggests the saltwater temperatures are generally higher. So the mean of tap water should be less than saltwater. The first option says tap water mean is greater, which is wrong. The second option says tap water mean is about \(4^\circ\) less, which aligns with the higher median and distribution of saltwater.

The saltwater (purple bars) has more trials at higher temperatures (\(102^\circ\text{C}\), \(103^\circ\text{C}\), \(104^\circ\text{C}\)) than tap water (blue bars). Given the median of saltwater (\(102^\circ\text{C}\)) is higher than tap water (\(100^\circ\text{C}\)), the mean of saltwater should be higher. The first statement (tap water mean > saltwater mean) is incorrect. The second statement (tap water mean ≈ \(4^\circ\) less) matches the distribution (higher temperatures for saltwater).

Answer:

The mean of the tap water boiling temperatures is about \(4^\circ\) less than the mean of the saltwater boiling temperatures.