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Question Number 58253 by pete last updated on 20/Apr/19
$$\mathrm{There}\:\mathrm{are}\:\mathrm{100},\:\mathrm{150}\:\mathrm{and}\:\mathrm{250}\:\mathrm{students}\:\mathrm{in} \\ $$$$\mathrm{forms}\:\mathrm{one},\:\mathrm{two}\:\mathrm{and}\:\mathrm{three},\:\mathrm{respectively} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{school}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{ages}\:\mathrm{of}\:\mathrm{tbe}\:\mathrm{students}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{forms}\:\mathrm{are}\:\mathrm{15}.\mathrm{6}\:\mathrm{years},\:\mathrm{16}.\mathrm{8}\:\mathrm{years}\:\mathrm{and} \\ $$$$\mathrm{18years}\:\mathrm{respectively},\:\mathrm{find} \\ $$$$\mathrm{i}.\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{forms} \\ $$$$\mathrm{ii}.\:\mathrm{correct}\:\mathrm{to}\:\mathrm{one}\:\mathrm{decimal}\:\mathrm{place},\:\mathrm{the}\:\mathrm{mean} \\ $$$$\mathrm{age}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{students} \\ $$
Answered by tanmay last updated on 20/Apr/19
$${N}={n}_{\mathrm{1}} +{n}_{\mathrm{2}} +{n}_{\mathrm{3}} =\mathrm{100}+\mathrm{150}+\mathrm{250}=\mathrm{500} \\ $$$${mean}=\overset{−} {{x}}=\frac{{n}_{\mathrm{1}} {x}_{\mathrm{1}} +{n}_{\mathrm{2}} {x}_{\mathrm{2}} +{n}_{\mathrm{3}} {x}_{\mathrm{3}} }{{n}_{\mathrm{1}} +{n}_{\mathrm{2}} +{n}_{\mathrm{3}} } \\ $$$$\overset{−} {{x}}=\frac{\mathrm{100}×\mathrm{15}.\mathrm{6}+\mathrm{150}×\mathrm{16}.\mathrm{8}+\mathrm{250}×\mathrm{18}}{\mathrm{500}} \\ $$$$=\frac{\mathrm{1560}+\mathrm{2520}+\mathrm{4500}}{\mathrm{500}} \\ $$$$=\frac{\mathrm{8580}}{\mathrm{500}}=\mathrm{17}.\mathrm{16} \\ $$
Commented by pete last updated on 20/Apr/19
$$\mathrm{thanks}\:\mathrm{sir} \\ $$
Commented by tanmay last updated on 20/Apr/19
$${most}\:{welcome}.. \\ $$