For $(2n+1)$ observations ${x_1},\, - {x_1}$, ${x_2},\, - {x_2},\,.....{x_n},\, - {x_n}$ and $0$ where $x$’s are all distinct. Let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Then which of the following is always true
For $(2n+1)$ observations ${x_1},\, - {x_1}$, ${x_2},\, - {x_2},\,.....{x_n},\, - {x_n}$ and $0$ where $x$’s are all distinct. Let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Then which of the following is always true
- A
$S.D. < M.D.$
- B
$S.D. > M.D.$
- C
$S.D. = M.D.$
- D
Nothing can be said in general about the relationship of $S.D.$ and $M.D.$
Similar Questions
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 mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject
Mathematics
Physics
Chemistty
Mean
$42$
$32$
$40.9$
Standard deviation
$12$
$15$
$20$
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
| Subject | Mathematics | Physics | Chemistty |
| Mean | $42$ | $32$ | $40.9$ |
| Standard deviation | $12$ | $15$ | $20$ |
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The average marks of $10$ students in a class was $60$ with a standard deviation $4$, while the average marks of other ten students was $40$ with a standard deviation $6$. If all the $20$ students are taken together, their standard deviation will be
The average marks of $10$ students in a class was $60$ with a standard deviation $4$, while the average marks of other ten students was $40$ with a standard deviation $6$. If all the $20$ students are taken together, their standard deviation will be
The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80.$ Then which one of the following gives possible values of $a$ and $b$ $?$
The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80.$ Then which one of the following gives possible values of $a$ and $b$ $?$
- [AIEEE 2008]
In any discrete series (when all values are not same) the relationship between $M.D.$ about mean and $S.D.$ is
In any discrete series (when all values are not same) the relationship between $M.D.$ about mean and $S.D.$ is