If the scores of 3 students in a test are 5, 6 and 7, find the standard deviation of their scores
A
\(\frac{2}{3}\)
B
\(\frac{2}{3}\sqrt{3}\)
C
\(\sqrt{\frac{2}{3}}\)
D
\(\sqrt{\frac{3}{2}}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
(x) = \(\frac{5 + 6 + 7}{3}\)
= \(\frac{18}{3}\)
= 6
\(\begin{array}{c|c} scores(X) & \text{d = (x - x) deviation} & (deviation)^2\\\hline 5 & 5 - 6 & 1\\ 6 & 6 - 6 & 0 \\ 7 & 7 - 6 & 1\\ \hline & & 2\end{array}\)
S.D \(\sqrt{\frac{\sum d^2}{n}}\) where d = deviation = (x - x)
= \(\sqrt{\frac{2}{3}}\)
Source: Myschool Past Questions Archive (Record #31361)