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:
- A$78$
- B$210$
- C$225$
- D$88$
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Similar Questions
If each of the observations $x_{1}, x_{2}, \ldots, x_{n}$ is increased by $a$,where $a$ is a positive or negative number,show that the variance remains unchanged.
Difficult
View SolutionIf the variance of the frequency distribution is $160$,then the value of $c \in N$ is
$X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$ $f$ $2$ $1$ $1$ $1$ $1$ $1$
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
The standard deviation of $n$ observations $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ is $\sigma$. Then, the standard deviation of the observations $\lambda a_{1}, \lambda a_{2}, \ldots, \lambda a_{n}$ is
MediumWBJEE 2016
View SolutionThe variance for the first six prime numbers greater than $5$ is
The variance and mean of $15$ observations are respectively $6$ and $10$. If each observation is increased by $8$,then the new variance and new mean of the resulting observations are respectively:
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