If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -
- Avariance will be unchanged.
- Bnew variance will be $k$ times old variance.
- Cstandard deviation will be unchanged.
- Dnew standard deviation will be $k$ times old standard deviation.
Explore More
Similar Questions
The variance of the following frequency distribution is:
Class Interval $0$-$4$ $4$-$8$ $8$-$12$ $12$-$16$ $16$-$20$ Frequency $2$ $4$ $6$ $3$ $1$
| Class Interval | $0$-$4$ | $4$-$8$ | $8$-$12$ | $12$-$16$ | $16$-$20$ |
| Frequency | $2$ | $4$ | $6$ | $3$ | $1$ |
Let $n$ be an odd natural number such that the variance of $1, 2, 3, 4, \ldots, n$ is $14$. Then $n$ is equal to ..... .
The diameters of circles (in mm) drawn in a design are given below:
Diameters $33-36$ $37-40$ $41-44$ $45-48$ $49-52$ No. of circles $15$ $17$ $21$ $22$ $25$
Calculate the standard deviation and mean diameter of the circles.
[ Hint : First make the data continuous by making the classes as $32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5$ and then proceed.] (in $\text{ mm}$)
| Diameters | $33-36$ | $37-40$ | $41-44$ | $45-48$ | $49-52$ |
| No. of circles | $15$ | $17$ | $21$ | $22$ | $25$ |
Calculate the standard deviation and mean diameter of the circles.
[ Hint : First make the data continuous by making the classes as $32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5$ and then proceed.] (in $\text{ mm}$)
Medium
View SolutionThe standard deviation of the following distribution is:
Class interval $0-10$ $10-20$ $20-30$ $30-40$ Frequency $1$ $3$ $4$ $2$
| Class interval | $0-10$ | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $1$ | $3$ | $4$ | $2$ |
The variance of the following continuous frequency distribution is
Class Interval $0-10$ $10-20$ $20-30$ $30-40$ Frequency $2$ $3$ $4$ $1$
| Class Interval | $0-10$ | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $2$ | $3$ | $4$ | $1$ |
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo