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There are five numbers 2, 3, 4, 5 and 6. The average value ?avg and root mean square (rms) value ?rms of these numbers are

A.
?avg = 4 & ?rms = 4
B.
?avg = 4 & ?rms = 4.242
C.
?avg = 5 & ?rms = 4
D.
?avg = 4 & ?rms = 5

Solution:

Concept:Average value (navg):It is defined as the average or mean of all data which are taken into consideration and mathematically it is given as:\(n_{avg}=\frac {some~ of ~all ~data}{Total ~number ~of ~data}\)Root Mean Square value (nrms): It is defined as root mean square of given data i.e. square root of the mean of squares of given data. It is given as:\(n_{rms}= \sqrt {\frac {sum~ of ~squares ~of~ all ~data}{number~ of ~data}}\)Calculation:Given:Numbers: 2, 3, 4, 5, 6\(n_{avg}=\frac {some~ of ~all ~data}{Total ~number ~of ~data}=\frac {2+3+4+5+6}{5}=\frac{20}5=4\)and\(n_{rms}= \sqrt {\frac {sum~ of ~squares ~of~ all ~data}{number~ of ~data}}=\sqrt {\frac {2^2+3^2+4^2+5^2+6^2}{5}}=\sqrt{\frac {90}5}=4.242\)

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