For a frequency distribution,the standard deviation is computed by applying the formula:
- A$\sigma = \sqrt{\left(\frac{\sum fd}{\sum f}\right) - \frac{\sum fd^2}{\sum f}}$
- B$\sigma = \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd^2}{\sum f}\right)^2}$
- C$\sigma = \sqrt{\left(\frac{\sum fd}{\sum f}\right)^2 - \frac{\sum fd^2}{\sum f}}$
- D$\sigma = \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd}{\sum f}\right)^2}$
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$X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$ $f$ $2$ $1$ $1$ $1$ $1$ $1$
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
The variance of $20$ observations is $5$. If each observation is multiplied by $2$,find the new variance of the resulting observations.
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