For the frequency distribution:
Variate $(x)$ $x_{1}$ $x_{2}$ $x_{3} \ldots x_{15}$ Frequency $(f)$ $f_{1}$ $f_{2}$ $f_{3} \ldots f_{15}$
where $0 < x_{1} < x_{2} < x_{3} < \ldots < x_{15} = 10$ and $\sum_{i=1}^{15} f_{i} > 0$,the standard deviation cannot be:
| Variate $(x)$ | $x_{1}$ | $x_{2}$ | $x_{3} \ldots x_{15}$ |
| Frequency $(f)$ | $f_{1}$ | $f_{2}$ | $f_{3} \ldots f_{15}$ |
where $0 < x_{1} < x_{2} < x_{3} < \ldots < x_{15} = 10$ and $\sum_{i=1}^{15} f_{i} > 0$,the standard deviation cannot be:
- A$2$
- B$1$
- C$4$
- D$6$
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Similar Questions
The variance of $10$ observations is $16$. If each observation is doubled,then the standard deviation of the new data will be -
Medium
View SolutionIf the variance of the frequency distribution is $160$,then the value of $c \in N$ is
$X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$ $f$ $2$ $1$ $1$ $1$ $1$ $1$
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
What is the standard deviation of the following series?
Class $0-10$ $10-20$ $20-30$ $30-40$ Frequency $1$ $3$ $4$ $2$
| Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $1$ | $3$ | $4$ | $2$ |
Medium
View SolutionLet $x_1, x_2, x_3, \dots, x_n$ be $n$ observations,$\bar{x}$ be their arithmetic mean,and $\sigma^2$ be their variance.
Statement $-1$: The variance of observations $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\sigma^2$.
Statement $-2$: The arithmetic mean of $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\bar{x}$.
Statement $-1$: The variance of observations $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\sigma^2$.
Statement $-2$: The arithmetic mean of $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\bar{x}$.
Difficult
View SolutionIf $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?
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