## Calculating a Geometric MeanConsider a sample of positive numbers
x G Let A G G The logarithm of the geometric mean is the arithmetic mean of the log transformed data: log(G The geometric mean is an appropriate measure of central tendency when averages of rates or index numbers are required. For example, suppose that, in three successive years the return
on an investment is 5%, 20% and
((1.05)(1.20)(0.96)) Therefore, the average rate of return (compound annual growth rate) is 6.5%. ## ExampleThis example is from J. Freund, F. Williams, B. Perles and C. Sullivan
[ The SHAZAM commands
(
The SHAZAM output can be viewed. The output shows the following results:
[SHAZAM Guide home] ## SHAZAM output|_SAMPLE 1 7 |_READ PRICE / BYVAR LIST 1 VARIABLES AND 7 OBSERVATIONS STARTING AT OBS 1 PRICE 137.0000 146.0000 163.0000 98.00000 144.0000 292.0000 119.0000 |_* Calculate the arithmetic mean and median |_STAT PRICE / MEAN=AN PMEDIAN NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM PRICE 7 157.00 63.082 3979.3 98.000 292.00 VARIABLE = PRICE MEDIAN = 144.00 LOWER 25%= 119.00 UPPER 25%= 163.00 INTERQUARTILE RANGE= 44.00 MODE NOT APPLICABLE |_* Calculate the geometric mean |_GENR LPRICE=LOG(PRICE) |_STAT LPRICE / MEAN=LGN NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM LPRICE 7 5.0011 0.34044 0.11590 4.5850 5.6768 |_GEN1 GN=EXP(LGN) |_PRINT AN GN AN 157.0000 GN 148.5828 |_STOP [SHAZAM Guide home] |