The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3, 4$ and $5$, were found to be incorrect . If the incorrect observations are omitted, then the variance of the remaining observations is
The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3, 4$ and $5$, were found to be incorrect . If the incorrect observations are omitted, then the variance of the remaining observations is
- [JEE MAIN 2017]
- A
$8.25$
- B
$8.50$
- C
$8$
- D
$9$
Similar Questions
The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4$ and $4;$ then the absolute value of the difference of the other two observations, is
The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4$ and $4;$ then the absolute value of the difference of the other two observations, is
- [JEE MAIN 2019]
The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$
Height
Weight
Mean
$162.6\,cm$
$52.36\,kg$
Variance
$127.69\,c{m^2}$
$23.1361\,k{g^2}$
Can we say that the weights show greater variation than the heights?
The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$
| Height | Weight | |
| Mean | $162.6\,cm$ | $52.36\,kg$ |
| Variance | $127.69\,c{m^2}$ | $23.1361\,k{g^2}$ |
Can we say that the weights show greater variation than the heights?
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 $\left[\mu^2+\sigma^2\right]$ is equal $.........$.
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 $\left[\mu^2+\sigma^2\right]$ is equal $.........$.
- [JEE MAIN 2023]
The variance of the first $n$ natural numbers is
The variance of the first $n$ natural numbers is
Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.
Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.