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\(\begin{array}{c|c} class 1 - 3 4 - 6 7 - 9\\ \hline Frequency 5 8 ...
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\(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)
Find the standard deviation of the data using the table above
A.
5
B.
\(\sqrt{60}\)
C.
\(\frac{5}{3}\)
D.
\(\sqrt{5}\)
Show Answer
Show Explanation
Correct Answer: A
Explanation
\(\begin{array}{c|c} \text{class intervals} & Fre(F) & \text{class-marks(x)} & Fx & (x - x)& (x - x)^2 & F(x - x)^2 \\ \hline 1 - 3 & 5 & 10 & 10 & -3 & 9 & 90\\ 4 - 6 & 8 & 40 & 40 & 0 & 0 & 0 \\ 7 - 9 & 5 & 40 & 40 & 3 & 9 & 360 \\ \hline & 18 & & 90 & & & 450 \end{array}\)
x = \(\frac{\sum fx}{\sum f}\)
= \(\frac{90}{18}\)
= 5
S.D = \(\frac{\sum f(x - x)^2}{\sum f}\)
= \(\frac{450}{18}\)
= \(\sqrt{25}\)
= 5
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