Explain how the relationship between the mean and median provides information about the symmetry or skewness of the​ data"s distribution.

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The mean is affected by extreme​ values, while the median is not. If the data set is skewed to the​ right, then the median is less than the mean. If the data set is​ symmetric, the mean equals the median. If the data set is skewed to the​ left, the mean is less than the median.
Describe the sample variance using words rather than a formula. Do the same with the population variance.
The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
Can the variance of a data set ever be​ negative? Explain. Can the variance ever be smaller than the standard​ deviation? Explain.

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The variance of a data set cannot be negative because it is the sum of the squared deviations divided by a positive value. Variance can be smaller than the standard deviation if the variance is less than 1.
for any number k >_ 1, at least 100(1-1/k squared)% of the observations in any data set are within k standard deviations of the mean; the percentage value is typically conservative in that the actual percentages often considerably exceed the stated lower bound
The rules gives the approximate % of observations w/in 1 standard deviation (68%), 2 standard deviations (95%) and 3 standard deviations (99.7%) of the mean when the histogram is well approx. by a normal curve