Question

the mean of 9 observations are 13. the mean of first 5 observations is 11 and the mean of last five observations is 14 find the mean of fifith observation.​

Answer 1

mean=summation of all observations/total number of observations.

Step-by-step explanation:

$\frac{x_{1}+ x_{2} +x_{3}+ x_{4}+ x_{5}+ x_{6}+x_{7} +x_{8} + x_{9} }{9} =13\\x_{1}+ x_{2} +x_{3}+ x_{4}+ x_{5}+ x_{6}+x_{7} +x_{8} + x_{9}=117\\\\\frac{x_{1}+ x_{2} +x_{3}+ x_{4}+ x_{5}}{5} =11\\x_{1}+ x_{2} +x_{3}+ x_{4}+ x_{5}=55\\\frac{x_{5}+ x_{6}+x_{7} +x_{8} + x_{9}}{5} =14\\x_{5}+ x_{6}+x_{7} +x_{8} + x_{9}=70\\x_{1}+ x_{2} +x_{3}+ x_{4}+ x_{5}+x_{5}+ x_{6}+x_{7} +x_{8} + x_{9}=55+70\\117+x_{5} =125\\x_{5}=8$

so value of fifth observation is 8.