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 
be the price per unit in period 
, 
be the quantity produced in period 
, and 
be the value of the 
units. Let 
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 |
 |
 |
| Fisher index |
 |
 |
| geometric mean index |
 |
![[product((p_n)/(p_0))^(v_0)]^(1/sumv_0)](https://mathworld.wolfram.com/images/equations/IndexNumber/Inline13.gif) |
| harmonic mean index |
 |
 |
| Laspeyres' index |
 |
 |
| marshall-Edgeworth index |
 |
 |
| mitchell index |
 |
 |
| Paasche's index |
 |
 |
| Walsh index |
 |
 |
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.
