\(\begin{array}{c|c}
Class Interval & 3 – 5 & 6 – 8 & 9 – 11 \\ \hline Frequency & 2 & 2 & 2 \end{array}\). Find the standard deviation of the above distribution.
- √5
-
√6
- √7
- √2
The correct answer is: B
Explanation
\(\begin{array}{c|c}Class Interval & 3 - 3 & 6 - 8 & 9 - 11 \\ x & 4 & 7 & 10 \\ f & 2 & 2 & 2 \\ f - x & 8 & 14 & 20 \\ |x - \bar{x}|^2 & 9 & 0 & 9 \\ |x - \bar{x}|^2 & 18 0 & 18 \end{array}\)\(\bar{x}\) = \(\frac {\sum fx}{\sum f}\)
= \(\frac {8 + 14 + 20}{2 + 2 + 2}\)
= \(\frac{42}{6}\)
\(\bar{x}\) = 7
S.D = \(\sqrt\frac{\sum f(x - \bar{x})^2}{\sum f}\)
= \(\sqrt\frac{18 + 0 + 18}{6}\)
= \(\sqrt\frac{36}{6}\)
= \(\sqrt {6}\)
There is an explanation video available .