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

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The median is affected by extreme values, when the typical is not. If the data collection is skewed to the right, then the median is less than the mean. If the data collection is symmetric, the mean amounts to the median. If the data collection is skewed to the left, the typical is much less than the median.

Describe the sample variance using words quite than a formula. Execute the same with the populace variance.

The sample variance is the amount of the squared deviations indigenous the mean divided by the variety of measurements minus one. The populace variance is the mean of the squared ranges of the dimensions on all units in the population from the mean.

Can the variance the a data collection ever be negative? Explain. Have the right to the variance ever before be smaller than the standard deviation? Explain.

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The variance of a data set cannot be an adverse because the is the sum of the squared deviations split by a confident value. Variance deserve to be smaller sized than the typical deviation if the variance is less than 1.

for any kind of number k >_ 1, at least 100(1-1/k squared)% of the observations in any kind of data set are within k traditional deviations of the mean; the percent value is typically conservative in that the really percentages often significantly exceed the proclaimed lower bound

The rules offers the approximate % of observations w/in 1 traditional deviation (68%), 2 traditional deviations (95%) and also 3 conventional deviations (99.7%) that the average when the histogram is fine approx. By a common curve

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