There is some speculation that a simple name change can result in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). Suppose that to test the profitability of name changes, we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.82%, with a standard deviation of 0.11%. Suppose that this mean and standard deviation apply to the population of all companies that changed names. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names.
| (a)According to Chebyshev's theorem, at least ▼(Choose one) of the relative increases in stock price lie between
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| (b)According to Chebyshev's theorem, at least ▼(Choose one) of the relative increases in stock price lie between
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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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