The $S.D.$ of a variate $x$ is $\sigma$. The $S.D.$ of the variate $\frac{ax + b}{c}$,where $a, b, c$ are constants,is
- A$\left( \frac{a}{c} \right) \sigma$
- B$\left| \frac{a}{c} \right| \sigma$
- C$\left( \frac{a^2}{c^2} \right) \sigma$
- DNone of these
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Similar Questions
The standard deviation of the numbers $22, 26, 28, 20, 24, 30$ is
The mean and standard deviation of $10$ observations are $20$ and $2$ respectively. Later on,it was observed that one observation was recorded as $50$ instead of $40$. Then the correct variance is:
DifficultJEE MAIN 2023
View SolutionThe variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is
Find the mean and variance for the following data:
$x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$ $f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$
| $x_i$ | $6$ | $10$ | $14$ | $18$ | $24$ | $28$ | $30$ |
| $f_i$ | $2$ | $4$ | $7$ | $12$ | $8$ | $4$ | $3$ |
Medium
View SolutionThe variance of the following frequency distribution is
Class Interval Frequency $0 - 6$ $10$ $6 - 12$ $8$ $12 - 18$ $6$ $18 - 24$ $4$ $24 - 30$ $2$
| Class Interval | Frequency |
|---|---|
| $0 - 6$ | $10$ |
| $6 - 12$ | $8$ |
| $12 - 18$ | $6$ |
| $18 - 24$ | $4$ |
| $24 - 30$ | $2$ |
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