Question

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.

Explanation:

Step1: Calculate the total number of tap - water trials

Add up the number of tap - water trials: \(3 + 6+7 + 6+2=24\) (using the heights of the blue bars).

Step2: Estimate the sum of tap - water boiling temperatures

$$
LATEXBLOCK0
$$

Step3: Calculate the mean of tap - water boiling temperatures

The mean of tap - water boiling temperatures is \(\frac{2400}{24}=100\) (since \(\text{Mean}=\frac{\text{Sum of values}}{\text{Number of values}}\)).

Step4: Calculate the total number of salt - water trials

Add up the number of salt - water trials: \(3+2 + 6+6+4+1=22\) (using the heights of the white bars).

Step5: Estimate the sum of salt - water boiling temperatures

$$
LATEXBLOCK1
$$

Step6: Calculate the mean of salt - water boiling temperatures

The mean of salt - water boiling temperatures is \(\frac{1630}{22}\approx74.09\) (this is wrong, let's do it correctly).

Correct way for salt - water:

$$
LATEXBLOCK2
$$

Correct calculation for salt - water:

$$
LATEXBLOCK3
$$

Another intuitive way (using median as a reference and distribution):
The median of tap - water is \(100^{\circ}C\) and the median of salt - water is \(102^{\circ}C\). Looking at the distribution:

• For tap - water: most of the values are around \(98 - 102\) with a median of \(100\).
• For salt - water: most of the values are around \(100 - 104\) with a median of \(102\).

The difference between the medians is \(102 - 100=2\). Since the distributions are somewhat symmetric (from the bar - chart appearance), the difference in means will be close to the difference in medians.

Answer:

The mean of the tap water boiling temperatures is about \(2^{\circ}\) less than the mean of the saltwater boiling temperatures.