\(\begin{array}{c|c} class& 1 – 3 & 4 – 6 & 7 – 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)
Find the standard deviation of the data using the table above
- 5
- \(\sqrt{6}\)
- \(\frac{5}{3}\)
-
\(\sqrt{5}\)
The correct answer is: D
Explanation
\(\begin{array}{c|c} \text{class intervals} & Fre(F) & \text{class-marks(x)} & Fx & (x - x)& (x - x)^2 & F(x - x)^2 \\ \hline 1 - 3 & 5 & 2 & 10 & -3 & 9 & 45\\ 4 - 6 & 8 & 5 & 40 & 0 & 0 & 0 \\ 7 - 9 & 5 & 8 & 40 & 3 & 9 & 45 \\ \hline & 18 & & 90 & & & 90 \end{array}\)
x = \(\frac{\sum fx}{\sum f}\)
= \(\frac{90}{18}\)
= 5
S.D = \(\frac{\sum f(x - x)^2}{\sum f}\)
= \(\frac{90}{18}\)
= \(\sqrt{5}\)