If both the means and the standard deviation of $50$ observations $x_1, x_2, ………, x_{50}$ are equal to $16$ , then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, …., (x_{50} - 4)^2$ is
The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -
Find the standard deviation for the following data:
${x_i}$ | $3$ | $8$ | $13$ | $18$ | $25$ |
${f_i}$ | $7$ | $10$ | $15$ | $10$ | $6$ |
Let $9 < x_1 < x_2 < \ldots < x_7$ be in an $A.P.$ with common difference $d$. If the standard deviation of $x_1, x_2 \ldots$, $x _7$ is $4$ and the mean is $\overline{ x }$, then $\overline{ x }+ x _6$ is equal to:
The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
If wrong item is omitted.