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]
  • A

    $150$

  • B

    $152$

  • C

    $153$

  • D

    $151$

Similar Questions

If the variance of the frequency distribution is $3$ then $\alpha$ is ......

$X_i$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
Frequency $f_i$ $3$ $6$ $16$ $\alpha$ $9$ $5$ $6$

 

  • [JEE MAIN 2023]

The mean and $S.D.$ of the marks of $200$ candidates were found to be $40$ and $15$ respectively. Later, it was discovered that a score of $40$ was wrongly read as $50$. The correct mean and $S.D.$ respectively are...

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively $A$ new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding 2 to each element of B. Then the sum of the mean and variance of the elements of $C$ is $.......$.

  • [JEE MAIN 2023]

Find the mean, variance and standard deviation using short-cut method

Height in cms $70-75$ $75-80$ $80-85$ $85-90$ $90-95$ $95-100$ $100-105$ $105-110$ $110-115$
No. of children $3$ $4$ $7$ $7$ $15$ $9$ $6$ $6$ $3$

Let the mean and the variance of $5$ observations $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first $4$ observation are $\frac{7}{2}$ and $a$ respectively, then $\left(4 a+x_{5}\right)$ is equal to

  • [JEE MAIN 2022]