The mean of 6 distinct observations is 6.5 an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the $6$ observations be $x_1, x_2, x_3, x_4, x_5, x_6$. Given $x_1=2, x_2=4, x_3=5, x_4=7$. Let $x_5=a$ and $x_6=b$.The mean $\bar{x} = \frac{

Vedclass · Accepted Answer

$10, 11$

Vedclass · Answer

(A) Let the $6$ observations be $x_1, x_2, x_3, x_4, x_5, x_6$. Given $x_1=2, x_2=4, x_3=5, x_4=7$. Let $x_5=a$ and $x_6=b$.The mean $\bar{x} = \frac{2+4+5+7+a+b}{6} = 6.5$.$18+a+b = 39$ $\Rightarrow a+b = 21$ $\Rightarrow b = 21-a$.The variance $\sigma^2 = \frac{\sum x_i^2}{n} - (\bar{x})^2 = 10.25$.$\frac{2^2+4^2+5^2+7^2+a^2+b^2}{6} - (6.5)^2 = 10.25$.$\frac{4+16+25+49+a^2+b^2}{6} = 10.25 + 42.25 = 52.5$.$94 + a^2 + b^2 = 315 \Rightarrow a^2 + b^2 = 221$.Substitute $b = 21-a$: $a^2 + (21-a)^2 = 221$.$a^2 + 441 - 42a + a^2 = 221$.$2a^2 - 42a + 220 = 0 \Rightarrow a^2 - 21a + 110 = 0$.$(a-10)(a-11) = 0$.Thus,the observations are $10$ and $11$.

The mean of $6$ distinct observations is $6.5$ and their variance is $10.25$. If $4$ out of $6$ observations are $2, 4, 5$ and $7$,then the remaining two observations are:

Similar Questions

The mean of $5$ numbers is $18$. If one number is excluded,their mean becomes $16$. Then the excluded number is

Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, 67$ $(a > b)$ are $40$ and $21$,respectively. If the mean deviation about the median is $26$,then $2a$ is equal to:

The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is

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. If the incorrect observation $8$ is replaced by $12$,calculate the correct mean and standard deviation.

For $(2n+1)$ observations ${x_1}, -{x_1}, {x_2}, -{x_2}, ....., {x_n}, -{x_n}$ and $0$,where all $x_i$ are distinct,let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Which of the following is always true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module