Suppose a population A has 100 observations 101,102, . . .,200 and another population B has 10

English

Gujarati

Hindi

13.Statistics

medium

Suppose a population $A $ has $100$ observations $ 101,102, . . .,200 $ and another population $B $ has $100$ observation $151,152, . . .,250$ .If $V_A$ and $V_B$ represent the variances of the two populations , respectively then $V_A / V_B$ is

A

$1$

B

$\frac{9}{4}$

C

$\frac{4}{9}$

D

$\frac{2}{3}$

(AIEEE-2006)

Solution

Series $A=101,102 \ldots \ldots 200$

Series $\mathrm{B}=151,152 \ldots \ldots .250$

Here series $\mathrm{B}$ can be obtained if we change the origin of $A$ by $50$ units.

And we know the variance does not change by changing the origin.

So, $\quad V_{A}=V_{B}$

$\Rightarrow \quad \frac{V_{A}}{V_{B}}=1$

Standard 11

Mathematics

Share

Similar Questions

The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3, 4$ and $5$, were found to be incorrect . If the incorrect observations are omitted, then the variance of the remaining observations is

hard

(JEE MAIN-2017)

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

If wrong item is omitted.

hard

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$………$

hard

(JEE MAIN-2022)

If the mean and variance of the following data:

$6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^{2}$ is equal to:

medium

(JEE MAIN-2021)

If mean and standard deviation of $5$ observations $x_1 ,x_2 ,x_3 ,x_4 ,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1 ,x_2 ,…..,x_3$ and $-50$ is equal to

hard

(JEE MAIN-2019)