Finding Mean for Grouped Data When Class Intervals Are Not Given

Q. The weights of 10 students (in kilograms) are:

36, 45, 31, 52, 35, 40, 55, 60, 38, 44

Find the median weight. [2 MARKS]

Q.

The mean of prime numbers between 20 and 30 is:

1. 27

2. 25

3. 26

4. 21

Q. 4 rational numbers between 1/4 and 1/6

Q. Pranalee was practising for a 100 m running race. She ran 100 m distance 20 times. The time required, in seconds, for each attempt was as follows.
18, 17, 17, 16, 15, 16, 15, 14, 16, 15, 15, 17, 15, 16, 15, 17, 16, 15, 14, 15.
Find the mean of the times taken for running.

Q.

The arithmetic mean of 1, 2, 3, 4, 5, ……., n is ____.

1. $\frac{n-1}{2}$

2. $\frac{n}{2}$

3. $\frac{n+1}{2}$

4. $\frac{n}{2}+1$

Q. If the numbers 3, 5, 7, 4 have frequencies $x,x+4,x-3,x+8$ with their arithmetic mean of 4, then $x$ will be:

1. $\frac{5}{3}$
2. $\frac{7}{4}$
3. $\frac{2}{3}$
4. $\frac{11}{3}$

Q. Find the mean of 2a-3b and 2a+3b

Q.

If the mean of $6,4,x,13,10$ is $8$. Find the value of x.

Q.

The mean of first five odd numbers is

1. 5

2. 6

3. 4

4. 7

Q. The following are the marks obtained in Maths by students of Class 8:
51, 94, 34, 20, 50, 81, 81, 90, 76, 34, 51, 86, 93, 99, 26, 54, 85, 71, 88, 40, 44, 56, 55, 57, 78, 53, 81, 78, 65, 78.
The data have to be grouped to find the mean marks.
One of the class intervals made is 60-70.
What are the upper and the lower limits of the first class interval?
What is $\sum f_i$ ?

1. 8, 4, 20, 30, 28
2. 8, 4, 30, 20, 30
3. 10, 1, 0, 10, 30
4. 10, 4, 10, 0, 30

Q. The marks obtained by 40 students in class X of a certain school in a math paper of 50 marks total, are represented in the table. Find the mean using direct method.
$\begin{array}{cc}\text{Marks obtained}& \text{Number of students}\\ 0-10& 3\\ 10-20& 4\\ 20-30& 13\\ 30-40& 15\\ 40-50& 5\end{array}$

1. 29.9
2. 28.7
3. 25.2
4. 26.4

Q.

In a dance class of 12 student, one of them who is 15 yr old leaves the class and a new student is admitted. This change increases the average age of the class by 3 months. Then, age of the new student is

1. 16 yr

2. 20 yr

3. 17 yr

4. 18 yr

Q.

The following are the marks obtained in Maths by students of Class 8:
51, 94, 34, 20, 50, 81, 81, 90, 76, 34, 51, 86, 93, 99, 26, 54, 85, 71, 88, 40, 44, 56, 55, 57, 78, 53, 81, 78, 65, 78.
The data have to be grouped to find the mean marks.
One of the class intervals made is 60-70.
How many should such class intervals be prepared?
What is the frequency of the last class interval?
What is $\sum f_i$ ?

1. 8, 4, 28

2. 8, 4 , 30

3. 10, 1, 30

4. 10, 4, 30

Q.

The marks obtained by 40 students in class X of a certain school in a math paper of 50 marks total, are presented in the table. Find the mean using direct method.
$\begin{array}{cc}\text{Marks obtained}& \text{Number of students}\\ 0-10& 3\\ 10-20& 4\\ 20-30& 13\\ 30-40& 15\\ 40-50& 5\end{array}$

1. 28.75

2. 25.25

3. 29.95

4. 26.45

Q.

The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean.

$$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Numberofstudents& 3& 4& 13& 15& 5\end{array}$$

1. 28.75

2. 25.2

3. 26.4

4. 29.9

Q. The marks obtained by 40 students of class VIII in an examination are given below:

16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23

Divide the data into five groups, namely, 0-5, 5-10, 10-15, 15-20 and 20-25, where 0-5 means marks greater than or equal to 0 but less than 5 and similarly 5-10 means marks greater than or equal to 5 but less than 10, and so on. Prepare a frequency table for the grouped data.

Q. The range of the data: 11, 22, 33, 44 is:

1. 33
2. 22
3. 44
4. 30

Q. The mean of following distribution is

$x_i$	$10$	$12$	$15$	$25$
$f_i$	$2$	$3$	$7$	$8$

1. $18.50$
2. $18.05$
3. $18.15$
4. $18.25$

Q. Find the average of first 30 natural numbers.

Q.

The mean of a data is given by:

1. 

2. 

3. 

4. 

Q.

The average of 2 and 3 is:

1. 2.5

2. 2.6

3. 2.4

4. 2.1

Q. What is the mean of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 and 100??

Q. If two sides of a triangle are equal , then it has _____ equal angles. $\left[1\text{Mark}\right]$

Q. Choose the correct ascending order of angles for the triangle with side lengths as AB = 50 ft, BC = 44 ft, and AC = 29 ft.

Q.

If the mean of the following data is 17 then the value of p is ___.

$$\begin{array}{cccccc}{x}_i& \text{10}& \text{p}& \text{18}& \text{21}& \text{25}\\ f_i& \text{10}& \text{15}& \text{7}& \text{9}& \text{9}\end{array}$$

Q. In an isosceles $△ABC,AB=AC$ and $\angle BAC={30}^{\circ }$. Find the remaining angles.

Q.

A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy? ___

$$\begin{array}{cc}Studentageinterval& Numberofstudent\\ 8-10& 7\\ 10-12& 10\\ 12-14& 9\\ 14-16& 13\\ 16-18& 11\\ 18-20& 2\end{array}$$

Q. If the perimeter of triangle ABC is 14 cm such that AB = AC and BC = 6 cm, then find the length of AB. (2 marks)

Q. In $\Delta ABC$, if ∠A = 45° and ∠B = 65°, then the shortest side of the triangle is _______.