Question

what is the means of fi and xi and whhy it is important​

Answer 1

Answer:

A geometric mean is a mean or average which shows the central tendency of a set of numbers by using the product of their values. For a set of n observations, a geometric mean is the nth root of their product. The geometric mean G.M., for a set of numbers x1, x2, … , xn is given as

G.M. = (x1. x2 … xn)1⁄n

or, G. M. = (π i = 1n xi) 1⁄n = n√( x1, x2, … , xn).

The geometric mean of two numbers, say x, and y is the square root of their product x×y. For three numbers, it will be the cube root of their products i.e., (x y z) 1⁄3.

Relation Between Geometric Mean and Logarithms

In order to make our calculation easy and less time consuming we use the concept of logarithms in the calculation of geometric means.

Since, G.M. = (x1. x2 … xn) 1⁄n

Taking log on both sides, we have

log G.M. = 1⁄n (log ((x1. x2 … xn))

or, log G.M. = 1⁄n (log x1 + log x2 + … + log xn)

or, log G.M. = (1⁄n) ∑ i= 1n log xi

or, G.M. = Antilog(1⁄n (∑ i= 1n log xi)).

Geometric Mean of Frequency Distribution

For a grouped frequency distribution, the geometric mean G.M. is

G.M. = (x1 f1. x2 f2 … xn fn) 1⁄N , where N = ∑ i= 1n fi

Taking logarithms on both sides, we get

log G.M. = 1⁄N (f1 log x1 + f2 log x2 + … + fn log xn) = 1⁄N [∑ i= 1n fi log xi ].

Answer 2

Answer:

Fi __Frequency

Fi __FrequencyXi-The sum of class interval divides by 2

Fi __FrequencyXi-The sum of class interval divides by 2It is important because for finding mean mode median.

Fi __FrequencyXi-The sum of class interval divides by 2It is important because for finding mean mode median.Hope it helps