The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted a and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to $..........$.
The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted a and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to $..........$.
- [JEE MAIN 2023]
- A
$36$
- B
$35$
- C
$34$
- D
$37$
Similar Questions
Let $\mathrm{X}$ be a random variable with distribution.
$\mathrm{x}$
$-2$
$-1$
$3$
$4$
$6$
$\mathrm{P}(\mathrm{X}=\mathrm{x})$
$\frac{1}{5}$
$\mathrm{a}$
$\frac{1}{3}$
$\frac{1}{5}$
$\mathrm{~b}$
If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :
Let $\mathrm{X}$ be a random variable with distribution.
| $\mathrm{x}$ | $-2$ | $-1$ | $3$ | $4$ | $6$ |
| $\mathrm{P}(\mathrm{X}=\mathrm{x})$ | $\frac{1}{5}$ | $\mathrm{a}$ | $\frac{1}{3}$ | $\frac{1}{5}$ | $\mathrm{~b}$ |
If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :
- [JEE MAIN 2021]
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 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 $........$.
- [JEE MAIN 2023]
From the data given below state which group is more variable, $A$ or $B$ ?
Marks
$10-20$
$20-30$
$30-40$
$40-50$
$50-60$
$60-70$
$70-80$
Group $A$
$9$
$17$
$32$
$33$
$40$
$10$
$9$
Group $B$
$10$
$20$
$30$
$25$
$43$
$15$
$7$
From the data given below state which group is more variable, $A$ or $B$ ?
| Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
| Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
| Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
Find the mean and variance for the following frequency distribution.
Classes
$0-10$
$10-20$
$20-30$
$30-40$
$40-50$
Frequencies
$5$
$8$
$15$
$16$
$6$
Find the mean and variance for the following frequency distribution.
| Classes | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Frequencies | $5$ | $8$ | $15$ | $16$ | $6$ |
The variance of $20$ observations is $5 .$ If each observation is multiplied by $2,$ find the new variance of the resulting observations.
The variance of $20$ observations is $5 .$ If each observation is multiplied by $2,$ find the new variance of the resulting observations.