the median boiling temperature of the tap water is 100°c. the median boiling temperature of the salt water…
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 4° less than the mean of the saltwater boiling temperatures. the mean of the tap water boiling temperatures is about 2° less than the mean of the saltwater boiling temperatures. 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 3° less than the mean of the saltwater boiling temperatures.
Answer
Explanation:
Step1: Recall relationship between mean and median
In a symmetric distribution, mean = median. In a right - skewed distribution, mean > median. In a left - skewed distribution, mean < median.
Step2: Analyze tap water
The median boiling temperature of tap water is $100^{\circ}C$. Assume tap - water data is somewhat symmetric around the median.
Step3: Analyze salt water
The median boiling temperature of salt water is $102^{\circ}C$. Assume salt - water data is also somewhat symmetric around the median.
Step4: Compare means
Since the median of salt water ($102^{\circ}C$) is $2^{\circ}C$ higher than the median of tap water ($100^{\circ}C$) and assuming similar distribution shapes (symmetric), the mean of the tap water boiling temperatures is about $2^{\circ}$ less than the mean of the saltwater boiling temperatures.
Answer:
The mean of the tap water boiling temperatures is about 2° less than the mean of the saltwater boiling temperatures.