If standard deviation of numbers 2,3,a and 11 is 3.5 then which of following is true ?

English

Gujarati

Hindi

13.Statistics

medium

If the standard deviation of the numbers $ 2,3,a $ and $11$ is $3.5$ then which of the following is true ?

A

$3{a^2} - 34a + 91 = 0$

B

$\;3{a^2} - 23a + 44 = 0$

C

$3{a^2} - 26a + 55 = 0$

D

$\;3{a^2} - 32a + 84 = 0$

(JEE MAIN-2016)

Solution

$\mathrm{SD}=\sqrt{\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{\mathrm{n}}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}\right)^{2}}$

$\frac{49}{4}=\frac{4+9+a^{2}+121}{4}-\left(\frac{16+a}{4}\right)^{2}$

$3 a^{2}-32 a+84=0$

Standard 11

Mathematics

Share

Similar Questions

The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$

Height Weight

Mean $162.6\,cm$ $52.36\,kg$

Variance $127.69\,c{m^2}$ $23.1361\,k{g^2}$

Can we say that the weights show greater variation than the heights?

medium

The data is obtained in tabular form as follows.

${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$

${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

hard

The mean of two samples of size $200$ and $300$ were found to be $25, 10$ respectively their $S.D.$ is $3$ and $4$ respectively then variance of combined sample of size $500$ is :-

normal

If the variance of the first $n$ natural numbers is $10$ and the variance of the first m even natural numbers is $16$, then $m + n$ is equal to

hard

(JEE MAIN-2020)

Let $X _{1}, X _{2}, \ldots, X _{18}$ be eighteen observations such that $\sum_{ i =1}^{18}\left( X _{ i }-\alpha\right)=36 \quad$ and $\sum_{i=1}^{18}\left(X_{i}-\beta\right)^{2}=90,$ where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is $1,$ then the value of $|\alpha-\beta|$ is …… .

hard

(JEE MAIN-2021)