Question

the histogram represents the distributions of boiling temperatures, in degrees celsius, of tap water and a mixture of salt water.
boiling temperatures
the standard deviation of the tap water data is 1.129
the standard deviation of the salt water data is 1.107
which explains why the standard deviation is the best measure of variability to use to compare the data?
the two distributions are each nearly symmetric.
the distributions do not overlap on the same range of temperatures.
the distribution of salt water boiling temperatures is left - skewed.
the distribution of tap water boiling temperatures is right - skewed.

Explanation:

To determine why standard deviation is the best measure of variability, we analyze each option:

• Option 1: Standard deviation is suitable for symmetric (or near - symmetric) distributions. When distributions are nearly symmetric, mean and standard deviation are good measures of center and variability. Looking at the histogram, the two distributions (tap water and salt water boiling temperatures) seem nearly symmetric.
• Option 2: Overlap of ranges has no direct relation to why standard deviation is the best measure of variability.
• Option 3: If a distribution is left - skewed, median and inter - quartile range (IQR) are better measures of center and variability, not standard deviation.
• Option 4: If a distribution is right - skewed, median and IQR are better measures of center and variability, not standard deviation.

So, the fact that the two distributions are each nearly symmetric makes standard deviation the best measure of variability.

Answer:

The two distributions are each nearly symmetric.