Question

1) The mean age of 6 person is 14.5 years. The mean age of four of them is 13.25 years. If the age of the fifth person is 16 years, find the age of the sixth.
2) The mean monthly income of three members of a family is ₹8000. Another member of the family get a job, and his monthly salary is ₹10000. What is the mean monthly income of the four earning members of the family
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Answer 1

mean=$\frac{summation of all observations}{no.of observations}$

Step-by-step explanation:

$\frac{x_{1} +x_{2} +x_{3} +x_{4} +x_{5} +x_{6}}{6}=14.5\\ given\\\frac{x_{1} +x_{2} +x_{3} +x_{4} }{4} =13.25\\x_{123} +x_{123}+ x_{123} +x_{123} =13.25*4=53\\therefore\\ \frac{x_{1} +x_{2} +x_{3} +x_{4} +x_{5} +x_{6}}{6}=14.5\\\frac{53 +16+x_{6}}{6}=14.5\\53+16+x_{6}=14.5*6\\ 69+x_{6} =87\\x_{6} =18$

age of sixth person is 18

 2.

    $\frac{x_{1} +x_{2} +x_{3}}{3} =8000\\x_{1} +x_{2} +x_{3}=24000\\\frac{x_{1} +x_{2} +x_{3}+x_{4} }{4}\\=\frac{24000+10000 }{4}\\=\frac{34000}{4} \\=8500$

mean of four earning members = 8500