The average marks of 10 students in a class was 60 with a standar… - Vidyadip

MCQ

The average marks of $10$ students in a class was $60$ with a standard deviation $4$, while the average marks of other ten students was $40$ with a standard deviation $6$. If all the $20$ students are taken together, their standard deviation will be

A
$5$
B
$7.5$
C
$9.8$
✓
$11.2$

✓

Answer

Correct option: D.

$11.2$

d
$\mathrm{n}_{1}=10, \mathrm{n}_{2}=10$

average $\mathrm{m}_{1}=60, \mathrm{m}_{2}=40$

$\sigma_{1}=4, \sigma_{2}=6$

Standard deviation of combined series

$\sigma=\sqrt{\frac{n_{1} \sigma_{1}^{2}+n_{2} \sigma_{2}^{2}}{n_{1}+n_{2}}+\frac{n_{1} n_{2}\left(m_{1}-m_{2}\right)^{2}}{\left(n_{1}+n_{2}\right)^{2}}}$

$=\sqrt{\frac{10 \times 16+10 \times 36}{10+10}+\frac{10 \times 10(60-40)^{2}}{(10+10)^{2}}}$

$=\sqrt{8+18+100}=\sqrt{126}=11.2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the angle between the lines whose direction ratios are $2,-1 , 2$ and $a, 3, 5$ be $45^\circ $, then $a =$

A vector $\vec a$ has components $3 p$ and $1$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $\overrightarrow{\text { a }}$ has components $p +1$ and $\sqrt{10},$ then a value of $p$ is equal to

Three identical dice are rolled. The probability that same number will appear on each of them will be

Let a relation $R$ be defined by $R = \{(4, 5); (1, 4); (4, 6); (7, 6); (3, 7)\}$ then ${R^{ - 1}}oR$ is

If $\alpha$ satisfies the equation $x^2+x+1=0$ and $(1+\alpha)^7=\mathrm{A}+\mathrm{B} \alpha+\mathrm{C}^2, \mathrm{~A}, \mathrm{~B}, \mathrm{C} \geq 0$, then $5(3 A-2 B-C)$ is equal to..........................

$\int {\frac{{2x + 5}}{{\sqrt {7 - 6x - {x^2}} }}dx} = A\sqrt {7 - 6x - {x^2}} + B\,{\sin ^{ - 1}}\left( {\frac{{x + 3}}{4}} \right) + C$ (where $C$ is a constant of integration), then the ordered pair $(A, B)$ is equal to

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) - $arg $({z_2})$ is equal to

The equations of the tangents to the circle ${x^2} + {y^2} = 50$ at the points where the line $x + 7 = 0$ meets it, are

Let $a, b , c \in R$ be such that $a ^{2}+ b ^{2}+ c ^{2}=1$ If $a \cos \theta=b \cos \left(\theta+\frac{2 \pi}{3}\right)=\operatorname{ccos}\left(\theta+\frac{4 \pi}{3}\right)$ where $\theta=\frac{\pi}{9},$ then the angle between the vectors $a \hat{i}+b \hat{j}+c \hat{k}$ and $b \hat{i}+c \hat{j}+a \hat{k}$ is

Let $5$ digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.