Finding Median of Grouped Data When Class Intervals Are Not Given

Q. The mean and median of the numbers 1, 2, 3, 4, $y$, 8, 9, 10, 12 and $x$ written in increasing order are both 10, then the values of $x$ and $y$ are _____.

1. $x=15,y=36$
2. $x=39,y=12$
3. $x=15,y=36$
4. $x=39,y=15$

Q. 26. In a triangle ABC, AB = AC.show that the altitude AD is median also.

Q.

Find the median of the following cumulative frequency distribution:
$\begin{array}{ccc}x& frequency& Cumulativefrequency\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

1. 54

2. 55

3. 49.5

4. 53.5

Q. $3x+4y=10$ and $2x-2y=2$

1. $x=1,y=6$
2. $x=2,y=1$
3. $x=1,y=2$
4. $x=6,y=1$

Q. Question 15
Weekly income of 600 families is tabulated below ?
$\begin{array}{cc}Weeklyincome\left(inRs\right)& Numberoffamilies\\ 0-1000& 250\\ 1000-2000& 190\\ 2000-3000& 100\\ 3000-4000& 40\\ 4000-5000& 15\\ 5000-6000& 5\\ Total& 600\end{array}$
Compute the median income.

Q. Solve the following pair of equations by the elimination method and the substitution method:

1. $x=1$ and $y=-3$
2. $x=5$ and $y=2$
3. $x=4$ and $y=6$
4. $x=2$ and $y=-3$

Q. Solve:
$6x^2+5x-1=0$.

Q. Solve the given pair of equations by substitution method:

1. $(2,7)$
2. $(4,9)$
3. $(-6,2)$
4. $(-3,3)$

Q. Find median of the given observation: $25,14,28,30,25,15,32$.

1. $28$
2. $30$
3. $25$
4. $31$

Q. The inter quartile range of the observations $3,5,9,11,13,18,23,25,32$ and $39$ is

1. $24$
2. $31$
3. $16$
4. $8$

Q. Median divides the total frequency into _____ equal parts.

1. $2$
2. $3$
3. $4$
4. None of these

Q. Form the pair of linear equations for the following problem and find their solution by the substitution method.
The difference between two numbers is $26$ and one number is three times the other find them.

Q. What is the median of $7,10,7,5,9,10$?

1. $7$
2. $8$
3. $10$
4. $9$

Q. Solve the following equations by substitution method.

1. $x=0,y=2$
2. $x=0,y=3$
3. $x=1,y=3$
4. $x=5,y=2$

Q. If $-1$ is a zero of polynomial $p\left(x\right)=a{x}^2+x^2+x+4$ find the value of $-a$

Q. If $x=2^{\frac{1}{3}}+2^{\frac{2}{3}}$ then the value of $x^2-6x+6x$ is

1. $3$
2. $-2$
3. $6$
4. $2$

Q. Solve for $x$ and $y$: $y=2x+9$ and $7x+3y=-51$

1. $-3$
2. $-1$
3. $2$
4. $-4$

Q. Find median of the given observation: $35,20,55,27,15,40$.

1. $28$
2. $30$
3. $25$
4. $31$

Q. Solve the following pairs pf linear (simultaneous) equations using method of elimination by substitution:
$2x-3y+6=0$
$\Rightarrow 2x=3y-6$

Q. The following data have been arranged in ascending order of magnitude.
$63,66,69,x,x+2,76,89$ and $103$.
If the median of the given data is $71$, find the value of $x$.

1. $60$
2. $70$
3. $69$
4. None of these

Q. Median of $23$ observations is $52$, what would be the median after adding $3$ in each observations ?

1. $52$
2. $54$
3. $56$
4. $55$

Q. If the median of the following frequency distribution is $32.5$, find the missing frequencies.

Class interval	Frequency
0-10	$f_1$
10-20	5
20-30	9
30-40	12
40-50	$f_2$
50-60	3
60-70	2
Total	40

1. $3,6$
2. $4,9$
3. $2,8$
4. None of these

Q. Solve the following pair of equations by substitution method
$2x+5y=2$ and $x+2y=3$

Q. Solve the following pair of equation by the substitution method
$x+y=4$ and $2x+y=3$

1. 1 and -5
2. -1 and 5
3. 1 and 5
4. -1 and -5

Q. The following observations have been arranged in ascending order. If the median of these observations is $58$ find the value of $x$
$24,27,43,48,x-1,x+3,68,73,80,90$

1. $55$
2. $56$
3. $48$
4. $57$