From the data given below state which group is more variable, G_1… - Vidyadip

Question

From the data given below state which group is more variable, $G_1$ or $G_2$?

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Group $G_1$	9	17	32	33	40	10	9
Group $G_2$	10	20	30	25	43	15	7

✓

Answer

Let's first find the coefficient of variable for Group $G_1$

$CI$	$f$	$x$	$\text{u}=\frac{\text{x}-\text{A}}{\text{h}}$	$fu$	$u^2$	$fu^2$
10-20	9	15	-3	-27	9	81
20-30	17	25	-2	-34	4	68
30-40	32	35	-1	-32	1	32
40-50	33	45	0	0	0	0
50-60	40	55	1	40	1	40
60-70	10	65	2	20	4	40
70-80	9	75	3	27	9	81
	150			-6		342

Here, $N = 150, A = 45, \sum\text{f}_\text{i}\text{u}_\text{i}=-6,\ \sum\text{f}_\text{i}\text{u}_\text{i}^2=342$ and $h = 10$
$\therefore\text{Mean}=\overline{\text{x}}=\text{A+h}\Big(\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}\Big)$
$\Rightarrow\overline{\text{x}}=45+10\Big(\frac{-6}{150}\Big)=44.6$
$\text{Var}(\text{X})=\text{h}^2\bigg[\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}^2-\Big(\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}\Big)^2\bigg]$
$\text{Var}(\text{X})=100\bigg[\frac{342}{150}-\Big(\frac{-6}{150}\Big)^2\bigg]=227.84$
$\therefore\text{S.D.}=\sqrt{\text{Var}(\text{X})}=\sqrt{227.84}=15.09$
Coefficient of variation $=\frac{\text{S.D.}}{\overline{\text{x}}}\times100=\frac{15.09}{44.6}\times100=33.83$
Now, Let's first find the coefficient of variable for Group $G_2$

$CI$	$f$	$x$	$\text{u}=\frac{\text{x}-\text{A}}{\text{h}}$	$fu$	$u^2$	$fu^2$
10-20	10	15	-3	-30	9	902
20-30	20	25	-2	-40	4	80
30-40	30	35	-1	-30	1	30
40-50	25	45	0	0	0	0
50-60	43	55	1	43	1	43
60-70	15	65	2	30	4	60
70-80	7	75	3	21	9	63
	150			-6		366

Here, $N = 150, A = 45, \sum\text{f}_\text{i}\text{u}_\text{i}=-6,\ \sum\text{f}_\text{i}\text{u}_\text{i}^2=366$ and $h = 10$
$\therefore\text{Mean}=\overline{\text{x}}=\text{A+h}\Big(\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}\Big)$
$\Rightarrow\overline{\text{x}}=45+10\Big(\frac{-6}{150}\Big)=44.6$
$\text{Var}(\text{X})=\text{h}^2\bigg[\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}^2-\Big(\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}\Big)^2\bigg]$
$\text{Var}(\text{X})=100\bigg[\frac{366}{150}-\Big(\frac{-6}{150}\Big)^2\bigg]=243.84$
$\therefore\text{S.D.}=\sqrt{\text{Var}(\text{X})}=\sqrt{227.84}=15.62$
Coefficient of variation $=\frac{\text{S.D.}}{\overline{\text{x}}}\times100=\frac{15.09}{44.6}\times100=35.02$
$\therefore$ Group $G_2$ is more variable.

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

More "5 Marks Questions" from Statistics→Statistics — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$\text{a}(\cos\text{B}\cos\text{C}+\cos\text{A})=\text{b}(\cos\text{C}\cos\text{A}+\cos\text{B})\\=\text{c}(\cos\text{A}\cos\text{B}+\cos\text{C}).$

Find the sum of the following series to n terms:
$1 \times 2 + 2 \times 3 + 3 \times 4 + 4 \times 5 + ...$

Find the equation of the ellipse in the following case:
eccentricity $\text{e}=\frac{1}{2}$ and foci $(\pm2, 0)$

In each of the following find the equation of the hyperbola satisfying the given conditionsfoci $(\pm0,\pm\sqrt10),$ passing throught (2,3) [NCERT ] $$

$\Bigg|\cos\text{x}\cos\Big(\frac{\pi}{3}-\text{x}\Big)\cos\Big(\frac{\pi}{3}+\text{x}\Big)\Bigg|\leq\frac{1}{4}$ for all values of x.

Prove the following statement by principle of mathematical induction:
2n < (n + 2)! for all natural number n.

Prove the following statement by principle of mathematical induction:
$n^2< 2^n$ for all natural numbers $\text{n}\geq5$

$P_1, P_2$ are points on either of the two lines $\text{y} - \sqrt{3}|\text{x}| = 2$ at a distance of $5$ units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from$ P1 , P2$ on the bisector of the angle between the given lines.
$[$Hint: Lines are $\text{y} = \sqrt{3}\text{x} + 2$ and $\text{y} = -\sqrt{3}\text{x} + 2$ according as $\text{x} \geq 0$ or $x < 0. y-$ axis is the bisector of the angles between the lines. $P_1, P_2$ are the points on these lines at a distance of $5$ units from the point of intersection of these lines which have a point on $y-$axis as common foot of perpendiculars from these points. The y$-$coordinate of the foot of the perpendicular is given by $2 + 5 \cos30^\circ.]$

Find the eccentricity, coordinates of the foci, equation of the directrices and lenght of the latus-rectum of the hyperbola
$9\text{x}^{2}-16\text{y}^{2}=144$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\cos\sqrt{\text{x}}-\cos\sqrt{\text{a}}}{\text{x}-\text{a}}$