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Question Number 89907 by necxxx last updated on 19/Apr/20

If the sum of 4 numbers is between  53 and 57 then the arithmetic mean of  the numbers could be one of the  following    a)11.5 b)12 c)12.5 d)13 e)14

$${If}\:{the}\:{sum}\:{of}\:\mathrm{4}\:{numbers}\:{is}\:{between} \\ $$$$\mathrm{53}\:{and}\:\mathrm{57}\:{then}\:{the}\:{arithmetic}\:{mean}\:{of} \\ $$$${the}\:{numbers}\:{could}\:{be}\:{one}\:{of}\:{the} \\ $$$${following} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{1}\left..\mathrm{5}\:{b}\right)\mathrm{12}\:{c}\right)\mathrm{12}.\mathrm{5}\:{d}\right)\mathrm{13}\:{e}\right)\mathrm{14} \\ $$

Answered by MJS last updated on 19/Apr/20

x^− =((Σ_(j=1) ^n x_j )/n)  n=4; 53<Σ_(j=1) ^n x_j <57 ⇒ ((53)/4)<x^− <((57)/4) same as  13.25<x^− <14.25 ⇒ answer is e) 14

$$\overset{−} {{x}}=\frac{\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{j}} }{{n}} \\ $$$${n}=\mathrm{4};\:\mathrm{53}<\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{j}} <\mathrm{57}\:\Rightarrow\:\frac{\mathrm{53}}{\mathrm{4}}<\overset{−} {{x}}<\frac{\mathrm{57}}{\mathrm{4}}\:\mathrm{same}\:\mathrm{as} \\ $$$$\left.\mathrm{13}.\mathrm{25}<\overset{−} {{x}}<\mathrm{14}.\mathrm{25}\:\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:{e}\right)\:\mathrm{14} \\ $$

Commented by I want to learn more last updated on 20/Apr/20

Sir, help me check Q89908. Is the question possible?. I just want to know.

$$\mathrm{Sir},\:\mathrm{help}\:\mathrm{me}\:\mathrm{check}\:\mathrm{Q89908}.\:\mathrm{Is}\:\mathrm{the}\:\mathrm{question}\:\mathrm{possible}?.\:\mathrm{I}\:\mathrm{just}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}. \\ $$

Commented by necxxx last updated on 20/Apr/20

It′s clear and understandable sir. Thank you.

$${It}'{s}\:{clear}\:{and}\:{understandable}\:{sir}.\:{Thank}\:{you}. \\ $$

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