Grouped Frequency Distribution

Q.

The heights (in cm) of students of a class is tabulated below.
$\begin{array}{cc}\text{Height}& \text{Number of students}\\ 150-154& 4\\ 155-159& 3\\ 160-164& 2\\ 165-169& 1\\ 170-174& 2\\ 175-179& 2\\ 180-184& 4\\ 185-189& 2\\ Total& 20\end{array}$
Identify the correct option (s).

1. The class distribution is discontinuous

2. Number of students having height in range of 160-174 cm is 5

3. The data can not be changed into continuous class interval form

4. The range of data is 40

Q.

Arrange the given heights of 20 students in grouped distribution with a class interval of 5. The number of students above the height of 169cm is

___

Heights (in cm): 150, 153, 162, 170, 186, 153, 162, 180, 165, 150, 178, 156, 184, 176, 173, 186, 159, 183, 180, 156.

Q.

The last page number on the textbooks of different subjects in a class is given.

$$\begin{array}{cc}\text{Subject}& \text{Page Number}\\ \text{English}& 203\\ \text{Hindi}& 203\\ \text{Maths}& 152\\ \text{Physics}& 177\\ \text{Chemistry}& 225\\ \text{Biology}& 172\\ \text{Computer Sci.}& 185\\ \text{History}& 203\\ \text{Geography}& 172\\ \text{Moral Sci.}& 267\end{array}$$

Find the probability that the last page number ends in
(i) an odd number
(ii) an even number
(iii) a multiple of 3. [4 MARKS]

Q. If the class marks of a frequency distribution are $20,25,30,35,40$ and $45$, find the classes and their width.

1. $17.5-22.5,22.5-27.5,27.5-32.5,32.5-37.5,37.5-42.5,42.5-47.5$
   Width of the class is $5$
2. $17-22,22.5-27.5,28-32.5,33-37.5,38-42.5,43-47.5$
   Width of the class is $7$
3. $16-23,23-28.5,278-32,32-38,38-43,43-48$
   Width of the class is $5$
4. None of these
   

Q. The perimeter of an isosceles triangle is $42cm$ and its base is $\frac{3}{2}$ times each of the equal sides. Find the length of each side of the triangle, area of the triangle and height of the triangle.

Q.

Raju sold an article by giving a discount of 8% for Rs. 17, 940 and earn profit of 19.6 %. If he did not give discount then how much profit percentage he gets ?

Q. Peter made a frequency table of the scores of his students in an exam. In which class interval students get a high score?

1. $25-30$
2. $35-40$
3. $40-45$
4. $45-50$

Q. $5y^2-29y+20$

1. $(5y-4)(y-5)$
2. $(5y+4)(y-5)$
3. $(5y-4)(y+5)$
4. None of these

Q. $AB$ is a diameter of a circle and $C$ is any point on the circumference of the circle. Then

1. The area of $△ABC$ is maximum when it is isosceles
2. The area of $△ABC$ is minimum when it is isosceles
3. The perimeter of $△ABC$ is maximum when it is isosceles
4. None of these

Q. What will be the first class interval, if the fifth class interval is $60-65$, the fourth class interval is $55-60$ and a total number of classes is limited to five.

1. 
2. 
3. 
4.