TOPICS
Search

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.

indexabbr.formula
Bowley indexP_B1/2(P_L+P_P)
Fisher indexP_Fsqrt(P_LP_P)
geometric mean indexP_G[product((p_n)/(p_0))^(v_0)]^(1/sumv_0)
harmonic mean indexP_H(sump_0q_0)/(sum(p_0^2q_0)/(p_n))
Laspeyres' indexP_L(sump_nq_0)/(sump_0q_0)
marshall-Edgeworth indexP_(ME)(sump_n(q_0+q_n))/(sum(v_0+v_n))
mitchell indexP_M(sump_nq_a)/(sump_0q_a)
Paasche's indexP_P(sump_nq_n)/(sump_0q_n)
Walsh indexP_W(sumsqrt(q_0q_n)p_n)/(sumsqrt(q_0q_n) p_n)

See also

Bowley Index, Fisher Index, Geometric Mean Index, Harmonic Mean Index, Laspeyres' Index, Marshall-Edgeworth Index, Mitchell Index, Paasche's Index, Walsh Index

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Index Number

Cite this as:

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

Subject classifications