H Flashcards
calculate and interpret 'the proportion of observations falling within a specified number of standard deviations of the mean' (dispersion) using Chebyshev’s inequality;
Chebyshevs inequality
“an inequality using standard deviation as a measure of dispersion. The inequality gives the proportion of values within k standard deviations of the mean.”
Definition(calc): “for any distribution with finite variance, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 − 1/k2 for all k > 1.”
“illustrates the proportion of the observations that must lie within a certain number of standard deviations around the sample mean.”
Interpretation: Fact: “a two-standard-deviation interval around the mean must contain at least 75 percent of the observations, and a three-standard-deviation interval around the mean must contain at least 89 percent of the observations, no matter how the data are distributed.”
Chebys importance: Stems from its generality. It holds for samples and populations and for discreet and continuos data regardless of the shape of the distribution
“Chebyshev’s inequality gives the minimum percentage of observations that must fall within a given interval around the mean, but it does not give the maximum percentage.”
