Question

Means score of $25$ observations is $80$ and that of another 75 observations is $60$ The mean score of all observations taken together is

• A. $85$
• B. $5$
• C. $65$
• D. none of these

Answer 1

The correct option is C $65$

Mean of 25 observations is 80.

$\frac{1}{25}{\sum }_{i=1}^{25}{x}_i=80{\sum }_{i=1}^{25}{x}_i=80\ast 25=2000$

sum of 25 observations $=2000$

Mean of 75 observations is 60.

$\frac{1}{75}{\sum }_{j=1}^{75}{y}_j=60{\sum }_{j=1}^{75}{y}_j=60\ast 75=4500$

sum of 75 observations $=4500$

The mean score of all observations taken together is $=\frac{\left(Sumof25observations\right)+\left(Sumof75observations\right)}{Totalnumberofallobservationstakentogether}=\frac{{\sum }_{i=1}^{25}{x}_i+{\sum }_{j=1}^{75}{y}_j}{25+75}=\frac{2000+4500}{25+75}=\frac{6500}{100}=65$