Statistics

The variance of the first $50$ even natural numbers 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$\Sigma\,f_{i}=62$. If$\left[x\right]$…

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace…

A factory is operating in two shifts, day and night, with $70$and$30$workers, respectively.If per day mean wage of the day shift workers is, $₹54$ and per day mean wage of all the workers is $₹60$, then per day mean…

The mean age of $25$ teachers in a school is $40$ years. A teacher retires at the age of $60$ years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is $39$ years, then the…

Consider three observations $a,b$ and $c$ such that $b=a+c$. If the standard deviation of$a+2,c+2$is $d$,then which of the following is true?

The mean and variance of $7$observations are $8$ and $16$ respetively. If two observations are $6$ and $8,$then the variance of the remaining $5$ observations is :

If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is :

If the mean of the frequency distribution Class : $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequency : $2$ $3$ $x$ $5$ $4$ is $28$, then its variance is ________ .

If the mean and variance of the frequency distribution $x_{i}$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $f_{i}$ $4$ $4$ $\alpha\,$ $15$ $8$ $\beta\,$ $4$ $5$ are $9$ and $15.08$ respectively, then the value…

The mean and variance of the marks obtained by the students in a test are $10$and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2$. then…

In a set of $2n$ distinct observations, each of the observation below the median of all the observations is increased by $5$ and each of the remaining observations is decreased by $3$. Then, the mean of the new set of…