- 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
Find the values of $n$ and $X$ in each of the following cases:
$\sum\limits _{i=1}^{n}( x_{i} -10) =30$ and $\sum\limits _{i=1}^{n}( x_{i} -6) =150$.
Given:
$\sum\limits _{i=1}^{n}( x_{i} -10) =30$ and $\sum\limits _{i=1}^{n}( x_{i} -6) =150$.
To do:
We have to find the values of $n$ and $X$.
Solution:
We know that,
Mean $\overline{X}=\frac{Sum\ of\ the\ observations}{Number\ of\ observations}$
Therefore,
$\sum_{i=1}^{n}(x_{i}-10)=30$...........(i)
$\sum_{i=1}^{n}(x_{i}-6)=150$...........(ii)
From (i) and (ii), we get,
$n \bar{x}-10 n=30$........(iii)
$n \bar{x}-6 n=150$.........(iv)
Subtracting (iv) from (iii), we get,
$-4 n=-120$
$n=\frac{-120}{-4}$
$n=30$
From (iii),
$n \bar{x}-10 \times 30=30$
$30 \bar{x}=30+300$
$30 \bar{x}=330$
$\bar{x}=\frac{330}{30}$
$=11$
Advertisements