Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:
- A$\frac{\sigma_1-\sigma_2}{\sigma_2} \times 100$
- B$\frac{\sigma_1-\sigma_2}{\sigma_1} \times 100$
- C$\frac{\sigma_2-\sigma_1}{\sigma_2} \times 100$
- D$\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100$
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Similar Questions
If $x_1, x_2, ..., x_n$ 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 $n$?
Let $x_1, x_2, \ldots, x_{10}$ be ten observations such that $\sum_{i=1}^{10}(x_i-2)=30$,$\sum_{i=1}^{10}(x_i-\beta)^2=98$,$\beta > 2$ and their variance is $\frac{4}{5}$. If $\mu$ and $\sigma^2$ are respectively the mean and the variance of $2(x_1-1)+4\beta, 2(x_2-1)+4\beta, \ldots, 2(x_{10}-1)+4\beta$,then $\frac{\beta\mu}{\sigma^2}$ is equal to:
DifficultJEE MAIN 2025
View SolutionIf the mean of $100$ observations is $50$ and their standard deviation is $5$,then the sum of squares of all observations is
Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution: $X_i$ $0$ $1$ $2$ $3$ $4$ $5$ $f_i$ $k+2$ $2k$ $k^2-1$ $k^2-1$ $k^2-1$ $k-3$
where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to:
| $X_i$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| $f_i$ | $k+2$ | $2k$ | $k^2-1$ | $k^2-1$ | $k^2-1$ | $k-3$ |
DifficultJEE MAIN 2023
View SolutionFor the following frequency distribution,find the variance:
$X$ $5$ $6$ $7$ $8$ $10$ Frequency $3$ $7$ $4$ $2$ $4$
| $X$ | $5$ | $6$ | $7$ | $8$ | $10$ |
| Frequency | $3$ | $7$ | $4$ | $2$ | $4$ |
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