State the condition under which geometric mean cannot be found.
Answers
Explanation:
The arithmetic mean-geometric mean (AM-GM) inequality states that the arithmetic mean of non-negative real numbers is greater than or equal to the geometric mean of the same list. Further, equality holds if and only if every number in the list is the same. Mathematically, for a collection of nn non-negative real numbers a_1,a_2,...,a_na
1
,a
2
,...,a
n
, we have
\frac{ a_1 + a_2 + \cdots + a_n } { n}\ge\sqrt[n] { a_1 a_2 \ldots a_n} ,
n
a
1
+a
2
+⋯+a
n
≥
n
a
1
a
2
…a
n
,
with equality if and only if a_1=a_2=\cdots =a_na
1
=a
2
=⋯=a
n
.
This wiki page will familiarize you with the AM-GM inequality and its applications in several scenarios. We will also prove this inequality through several methods and further generalize it for deeper insights.
Answer:
The calculation of the Geometric Mean may appear impossible if one or more of the data points is zero (0). Often these zero values are really less than the limit of detection and are referred to as censored data.
Explanation:
The G.M for the given data set is always less than the arithmetic mean for the data set. If each object in the data set is substituted by the G.M, then the product of the objects remains unchanged. The ratio of the corresponding observations of the G.M in two series is equal to the ratio of their geometric means.