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In 1863, English economist William Stanley Jevons proposed taking the geometric average of the price relative of period t and base period 0. [5] When used as an elementary aggregate, the Jevons index is considered a constant elasticity of substitution index since it allows for product substitution between time periods.
The geometric mean of a non-empty data set of positive numbers is always at most their arithmetic mean. Equality is only obtained when all numbers in the data set are equal; otherwise, the geometric mean is smaller. For example, the geometric mean of 2 and 3 is 2.45, while their arithmetic mean is 2.5.
The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean. [1]
The average stock market return of about 10 percent doesn’t factor in the impact of inflation, which has historically been around 2 to 4 percent annually depending on the time period.
The geometric average return is equivalent to the cumulative return over the whole n periods, converted into a rate of return per period. Where the individual sub-periods are each equal (say, 1 year), and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.
For example, consider a period of a half of a year for which the return is −23% and a period of two and a half years for which the return is +13%. The average percentage return for the combined period is the single year return, R, that is the solution of the following equation: (1 − 0.23) 0.5 × (1 + 0.13) 2.5 = (1 + R) 0.5+2.5, giving an ...
A simple way to calculate the mean of a series of angles (in the interval [0°, 360°)) is to calculate the mean of the cosines and sines of each angle, and obtain the angle by calculating the inverse tangent. Consider the following three angles as an example: 10, 20, and 30 degrees.
Trump Media & Technology Group stock ()closed over 15% higher Friday and was briefly halted for volatility after Donald Trump said he would not sell his shares in the company, the home of Trump's ...