Let $x_{i} (1 \leq i \leq 10)$ be ten observations of a random variable $X$. If $\sum_{i=1}^{10} (x_{i} - p) = 3$ and $\sum_{i=1}^{10} (x_{i} - p)^{2} = 9$,where $0 \neq p \in R$,then the standard deviation of these observations is:
- A$\sqrt{\frac{3}{5}}$
- B$\frac{7}{10}$
- C$\frac{9}{10}$
- D$\frac{4}{5}$
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The coefficient of variation of the first $5$ prime numbers is
In an experiment with $15$ observations for $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:
The data is obtained in tabular form as follows:
$x_i$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$ $f_i$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$
Find the standard deviation of the given data. (in $.69$)
| $x_i$ | $60$ | $61$ | $62$ | $63$ | $64$ | $65$ | $66$ | $67$ | $68$ |
| $f_i$ | $2$ | $1$ | $12$ | $29$ | $25$ | $12$ | $10$ | $4$ | $5$ |
Find the standard deviation of the given data. (in $.69$)
Difficult
View SolutionThe mean and the standard deviation $(s.d.)$ of five observations are $9$ and $0,$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10,$ then their $s.d.$ is?
DifficultJEE MAIN 2018
View SolutionIf the mean of the discrete distribution $8, 9, 6, 5, x, 4, 6, 5$ is $6$,then its standard deviation (nearest to two decimal places) is
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