Question

the histogram represents the distributions of boiling temperatures, in degrees celsius, of tap water and a mixture of salt water. 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:

Standard deviation is a measure of variability that is most appropriate for symmetric distributions. When data is symmetric, the mean is a good central - tendency measure, and standard deviation effectively quantifies the spread around this mean. If the distributions were skewed (left - skewed or right - skewed), the median would be a better measure of central tendency, and other measures of variability (like the inter - quartile range) would be more appropriate. If the distributions did not overlap on the same range of temperatures, comparing standard deviations might not be as straightforward as the data sets would be in completely different "scales" in terms of temperature.

Answer:

The two distributions are each nearly symmetric.