the distribution of household income in the United States is not believed to be normally distributed but is instead right-skewed. Suppose that the mean income of US households is $92,300 with a standard deviation of $32,000.
(e) Why is the standard deviation of the mean income in the sample of 100 households that you computed in part (d) much lower than the population standard deviation of $32,000? -- (part (d) is suppose 100 households are randomly selected and the average income is calculated. what is the standard dev of the mean income in the sample of 100 households - I got 3200 for that.)
(f) Suppose 100 households are randomly selected and the average income in the sample is calculated. Based on the Central Limit Theorem, what is the approximate probability that the mean income in the sample of 100 households is less than $89,000?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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