The mean of five observations is 4 and their | vedclass

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

Question

(C) Let the five observations be $1, 2, 6, a,$ and $b$.Given that the mean $\bar{x} = 4$ and $n = 5$.$\bar{x} = \frac{1 + 2 + 6 + a + b}{5} = 4$$9 + a

Vedclass · Accepted Answer

$4$ and $7$

Vedclass · Answer

(C) Let the five observations be $1, 2, 6, a,$ and $b$.Given that the mean $\bar{x} = 4$ and $n = 5$.$\bar{x} = \frac{1 + 2 + 6 + a + b}{5} = 4$$9 + a + b = 20 \implies a + b = 11 \implies b = 11 - a$ ... $(1)$Given that the variance $\sigma^2 = 5.2$.$\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n} = 5.2$$\frac{(1-4)^2 + (2-4)^2 + (6-4)^2 + (a-4)^2 + (b-4)^2}{5} = 5.2$$(-3)^2 + (-2)^2 + (2)^2 + (a-4)^2 + (b-4)^2 = 26$$9 + 4 + 4 + (a-4)^2 + (b-4)^2 = 26$$17 + (a-4)^2 + (b-4)^2 = 26$$(a-4)^2 + (b-4)^2 = 9$ ... $(2)$Substitute $b = 11 - a$ into equation $(2)$:$(a-4)^2 + (11 - a - 4)^2 = 9$$(a-4)^2 + (7 - a)^2 = 9$$(a^2 - 8a + 16) + (49 - 14a + a^2) = 9$$2a^2 - 22a + 65 = 9$$2a^2 - 22a + 56 = 0$$a^2 - 11a + 28 = 0$$(a-4)(a-7) = 0$So,$a = 4$ or $a = 7$.If $a = 4$,then $b = 11 - 4 = 7$.If $a = 7$,then $b = 11 - 7 = 4$.Thus,the other two observations are $4$ and $7$.

Marks:	$2$	$3$	$5$	$7$
Frequency:	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

Class	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$3$	$\lambda$	$4$	$7$

List-$I$	List-$II$
$(P)$ The mean of the above data is	$(1) 2.5$
$(Q)$ The median of the above data is	$(2) 5$
$(R)$ The mean deviation about the mean of the above data is	$(3) 6$
$(S)$ The mean deviation about the median of the above data is	$(4) 2.7$
	$(5) 2.4$

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

Similar Questions

The mean income of a group of individuals is $400$ and the mean income of another group of individuals is $480$. If the mean income of all the individuals in both groups combined is $430$,find the ratio of the number of individuals in the two groups.

If for some $x \in R^{+} \cup \{0\}$,the frequency distribution of the marks obtained by $20$ students in a test is given by the table below,then find the mean of the marks.
Marks: $2$ $3$ $5$ $7$
Frequency: $(x+1)^2$ $2x-5$ $x^2-3x$ $x$

If the mean and the variance of the data are $\mu$ and $19$ respectively, then the value of $\lambda+\mu$ is:
Class $4-8$ $8-12$ $12-16$ $16-20$
Frequency $3$ $\lambda$ $4$ $7$

Which one of the following is false?

Vedclass Test Series

Exam Paper Generator

Online Exam Module