Lehmer Mean Calculator
Calculate the Lehmer mean, a generalization that includes harmonic, arithmetic, and contraharmonic means as special cases.
Enter Values
-20 (HM)1 (AM)2 (CM)4
Examples:
Lehmer Mean (p = 2)
6.000000
Special Cases:
Minimum (p → -∞):2.0000
Harmonic Mean (p = 0):3.840000
Arithmetic Mean (p = 1):5.000000
Contraharmonic (p = 2):6.000000
Maximum (p → +∞):8.0000
Calculation Details:
Sum(x^p):
120.0000
Sum(x^(p-1)):
20.0000
Count:
4
What is Lehmer Mean?
The Lehmer mean, named after Derrick Henry Lehmer, is a generalization of the weighted power mean. Unlike the power mean which uses the same power in numerator and denominator, the Lehmer mean uses consecutive powers. It provides another way to interpolate between different types of means by varying the parameter p.
Formula
Lp = Sum(x^p) / Sum(x^(p-1))
The Lehmer mean is a weighted mean where each value is weighted by x^(p-1).