Answer:
Hello,
Step-by-step explanation:
1) boys
[tex]\overline{x}=\dfrac{\displaystyle \sum_{i=1}^n\ x_i}{n}\\\\\Longrightarrow\ \displaystyle \sum_{i=1}^n\ x_i=n*\overline{x}=15*74=1110\\\\\\var=\sigma^2=\dfrac{\displaystyle \sum_{i=1}^n\ x_i^2}{n}-\overline{x}^2\\\\\Longrightarrow\ \displaystyle \sum_{i=1}^n\ x_i^2=n*(var+\overline{x}^2)=15*(1046.25+74^2)=97833,75\\[/tex]
2) females
[tex]\displaystyle \sum_{i=1}^n\ x_i=n*\overline{x}=12*77=924\\\\\displaystyle \sum_{i=1}^n\ x_i^2=n*(var+\overline{x}^2)=12*(948.64+77^2)=82531,68\\[/tex]
3)exam test
[tex]n=15+12=27\\\displaystyle \sum_{i=1}^n\ x_i=1110+924=2034\\\\\displaystyle \sum_{i=1}^n\ x_i^2=97833,75+82531,68=180365,43\\\\[/tex]
[tex]var=m_2-m_1^2=180365.43/27-75,33333333^2=1005,09[/tex]
