Index Number

A statistic which assigns a single number to several individual statistics in order to quantify trends. The best-known index in the United States is the consumer price index, which gives a sort of "average" value for inflation based on price changes for a group of selected products. The Dow Jones and NASDAQ indexes for the New York and American Stock Exchanges, respectively, are also index numbers.

Let p_n be the price per unit in period n, q_n be the quantity produced in period n, and v_n=p_nq_n be the value of the n units. Let q_a be the estimated relative importance of a product. There are several types of indices defined, among them those listed in the following table.

index abbr. formula

Bowley index P_B 1/2(P_L+P_P)

Fisher index P_F sqrt(P_LP_P)

geometric mean index P_G [product((p_n)/(p_0))^(v_0)]^(1/sumv_0)

harmonic mean index P_H [画像:(sump_0q_0)/(sum(p_0^2q_0)/(p_n))]

Laspeyres' index P_L (sump_nq_0)/(sump_0q_0)

marshall-Edgeworth index P_(ME) (sump_n(q_0+q_n))/(sum(v_0+v_n))

mitchell index P_M (sump_nq_a)/(sump_0q_a)

Paasche's index P_P (sump_nq_n)/(sump_0q_n)

Walsh index P_W [画像:(sumsqrt(q_0q_n)p_n)/(sumsqrt(q_0q_n) p_n)]

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References

Fisher, I. The Making of Index Numbers: A Study of Their Varieties, Tests and Reliability, 3rd ed. New York: Augustus M. Kelly, 1967.Kenney, J. F. and Keeping, E. S. "Index Numbers." Ch. 5 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 64-74, 1962.Mudgett, B. D. Index Numbers. New York: Wiley, 1951.

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Index Number

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Weisstein, Eric W. "Index Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IndexNumber.html

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