Let $x_1, x_2, \dots, x_n$ be the values taken by a variable $X$ and $y_1, y_2, \dots, y_n$ be the values taken by a variable $Y$ such that $y_i = ax_i + b$,where $i = 1, 2, \dots, n$. Then...
- A$V(Y) = a^2V(X)$
- B$V(Y) = a^2V(X) + b$
- CNone of these
- D$V(Y) = V(X) + b$
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Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=b$,where $a > b$,be $5$ and $10$ respectively. Then the Variance of the observations $n+x_n$ for $n=1, 2, 3, 4, 5$ is:
DifficultJEE MAIN 2025
View SolutionLet $n$ be an odd natural number such that the variance of $1, 2, 3, 4, \ldots, n$ is $14$. Then $n$ is equal to ..... .
If the variance of the frequency distribution is $160$,then the value of $c \in N$ is
$X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$ $f$ $2$ $1$ $1$ $1$ $1$ $1$
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
The marks obtained by students $A$ and $B$ in $3$ examinations are given below:
Marks of $A$ $30, 20, 40$ Marks of $B$ $70, 0, 5$
The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:
| Marks of $A$ | $30, 20, 40$ |
| Marks of $B$ | $70, 0, 5$ |
The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:
If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -
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