$\text{Assertion (A):}$ Variance of $4x_1, 4x_2, \ldots, 4x_n$ is $16$ times the variance of $x_1, x_2, \ldots, x_n$. $\text{Reason (R):}$ If $y = ax + b$,then variance of $y$ is $a(\text{variance of } x) + b$. The correct option among the following is
- A$(A)$ is true,$(R)$ is true and $(R)$ is the correct explanation for $(A)$.
- B$(A)$ is true,$(R)$ is true but $(R)$ is not the correct explanation for $(A)$.
- C$(A)$ is true but $(R)$ is false.
- D$(A)$ is false but $(R)$ is true.
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Similar Questions
The mean and the standard deviation of a data set of $8$ items are $25$ and $5$ respectively. If two items $15$ and $25$ are added to this data,then the variance of the new data is:
The variance $\sigma^2$ of the data is $ . . . . . .$
$x_i$ $0$ $1$ $5$ $6$ $10$ $12$ $17$ $f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$
| $x_i$ | $0$ | $1$ | $5$ | $6$ | $10$ | $12$ | $17$ |
| $f_i$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
If $\sum_{i = 1}^9 (x_i - 5) = 9$ and $\sum_{i = 1}^9 (x_i - 5)^2 = 45$,then the standard deviation of the $9$ items $x_1, x_2, ..., x_9$ is:
DifficultJEE MAIN 2018
View SolutionThe mean and standard deviation of $100$ items are $50$ and $4$ respectively. The sum of the squares of all the items is:
MediumKCET 2019
View SolutionIf each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$,where $k$ is a positive number,then the variance of the data:
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