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The trade-weighted effective exchange rate index is an economic indicator for comparing the exchange rate of a country against those of their major trading partners. By design, movements in the currencies of those trading partners with a greater share in an economy's exports and imports will have a greater effect on the effective exchange rate. [1]
As U. S. trade expanded over time, the weights in that index went unchanged and became out of date. To more accurately reflect the strength of the dollar relative to other world currencies, the Federal Reserve created the trade-weighted US dollar index, [3] which includes a bigger collection of currencies than the US dollar index. The regions ...
The Index goes up when the U.S. dollar gains "strength" (value) when compared to other currencies. [3] The index is designed, maintained, and published by ICE (Intercontinental Exchange, Inc.), with the name "U.S. Dollar Index" a registered trademark. [4] [5] It is a weighted geometric mean of the dollar's value relative to following select ...
Constant Dollars: weighted by a constant/unchanging basket/list of goods and services. Chained Dollars: weighted by a basket/list that changes yearly to more accurately reflect actual spending. The basket is an average of the basket for successive pairs of years; example of paired years are 2010–2011, 2011–2012, etc.
The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures , the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal.
The expected value of a random variable is the weighted average of the possible values it might take on, with the weights being the respective probabilities. More generally, the expected value of a function of a random variable is the probability-weighted average of the values the function takes on for each possible value of the random variable.
The degrees of freedom of this weighted, unbiased sample variance vary accordingly from N − 1 down to 0. The standard deviation is simply the square root of the variance above. As a side note, other approaches have been described to compute the weighted sample variance. [7]
Based on this sample, the estimated population mean is 10, and the unbiased estimate of population variance is 30. Both the naïve algorithm and two-pass algorithm compute these values correctly. Next consider the sample (10 8 + 4, 10 8 + 7, 10 8 + 13, 10 8 + 16), which gives rise to the same estimated variance as the first sample. The two-pass ...