Calculate AM, GM, and HM from the following data and also verify their relations among them for the following data:

Marks :	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
No. of students	$5$	$10$	$25$	$30$	$20$	$10$

 

Find the geometric mean of the values $10, 5, 14, 8, 15$.

If $n_1$ and $n_2$ are the sizes, $G_1$ and $G_2$ the geometric means of two series, respectively, then which one of the following expresses the geometric mean $\left(G\right)$ of the combined series?

Calculate the Geometric mean from the following data : 

$3, 13, 11, 15, 5, 4, 2$.

Find the geometric mean for the following data, which gives the defective screws obtained in a factory.

$\begin{array}{|ccccc|}\hline \text{ Diameter }\left(\mathrm{cm}\right)& 5& 15& 25& 35\\ \begin{array}{c}\text{ Number of defective }\\ \text{ screws }\end{array}& 5& 8& 3& 4\\ \hline\end{array}$

The geometric mean of the series $1,2,4,......,2^n$ is,

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

Geometric Mean is better than other means when?

Calculate the geometric and the harmonic mean of the following series of monthly expenditure of a batch of students.

$125,130,75,10,45,0.5,0.40,500,150,5$