![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Explain, by taking a suitable example, how the arithmetic mean alters by multiplying each term by a constant $k$.
To do:
We have to explain how the arithmetic mean alters by multiplying each term by a constant $k$.
Solution:
We know that,
Mean $\overline{X}=\frac{Sum\ of\ the\ observations}{Number\ of\ observations}$
Let $x_1, x_2, x_3, x_4$ and $x_5$ be five numbers whose mean is $\overline{X}$.
This implies,
$\overline{X}=\frac{x_1+x_2+x_3+x_4+x_5}{5}$
A constant $k$ is multiplied with each term.
Therefore,
New mean $=\frac{\left(x_{1}k\right)+\left(x_{2}k\right)+\left(x_{3}k\right)+\left(x_{4}k\right)+\left(x_{5}k\right)}{5}$
$=\frac{k(x_{1}+x_{2}+x_{3}+x_{4}+x_{5})}{5}$
$=\frac{k}{5}\times \frac{x_{1}+x_{2}+x_{3}+x_{4}+x_{5}}{5}$
$=\frac{k}{5}\bar{X}$