Mean of Grouped Frequency Distribution by Direct Method

Q.

The following table gives the marks obtained by $100$ students in a class test.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Number of Students	$12$	$18$	$27$	$20$	$17$	$6$

Find the mean marks scored by a student in class test.

Q. The following table shows the frequency distribution of the diameters of 40 bottles. Find the mean of the data.
$\begin{array}{cccccc}\text{Diameter (mm)}& 35-39& 40-44& 45-49& 50-54& 55-60\\ \text{Frequency}& 6& 12& 15& 10& 7\end{array}$

1. 45
2. 37
3. 55
4. 47

Q. Calculate the class mark of the given class intervals and match the following.

1. 22.5
2. 12.5
3. 17.5
4. 7.5

Q. The following table shows the frequency distribution of the diameters of 40 bottles. Find the mean of the data.
$\begin{array}{cccccc}\text{Diameter (mm)}& 35-39& 40-44& 45-49& 50-54& 55-60\\ \text{Frequency}& 6& 12& 15& 10& 7\end{array}$

1. 45
2. 37
3. 47
4. 55

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 is the frequency of the last class interval?

1. 2
2. 8
3. 5
4. 4

Q. There are three methods to find the mean of grouped data, they are the direct method, step deviation method and assumed mean method.

1. True
2. False

Q.

The marks obtained by 40 students in class X of a certain school in a math paper, are presented in the table.The total marks in that exam was 50. 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. 26.45

4. 29.95

Q. The average of the upper and lower class limits is called the class mark of that class.

1. False
2. True

Q. The following table shows the frequency distribution of the ages of 35 people. Find the mean of the data.
$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency\left(f\right)& 5& 15& 10& 2& 3\end{array}$

1. 16.5
2. 32.7
3. 20.1
4. 45.8

Q. Which of the following statements are true?
(i) Mean cannot be calculated for only two numbers.
(ii) There are three methods of finding the mean of grouped data.

1. (i)
2. (ii)
3. (i) and (ii)
4. Neither (i) nor (ii)

Q. For finding the mean value of the grouped data it is assumed that the frequency of each class interval is not centred around its mid-point.

1. False
2. True