Mean of Ungrouped Frequency Distribution by Direct Method

Q.

$\sum f_i{x}_i$ = 10$x$ + 40, $\sum f_i$ = 12. If the mean of the distribution is 60, what is the value of $x$?

1. 72

2. 68

3. 70

4. 74

Q.

Find the mean of the following data:

$20,40,60,80,100$

Q. The upper limit of a class interval is 2a and lower limit of the class interval is a. The ratio of class size and mid value will be

1. $1:4$
2. $2:3$
3. $2:3$
4. $1:2$

Q.

The distribution of height of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table.
$\begin{array}{ccccccc}Height& 110& 115& x_1& 120& 121& 125\\ Numberofstudents& 6& 8& 14& f_1& 4& 3\end{array}$

1. $x_1=118,f_1=15$

2. $x_1=121,f_1=15$

3. $x_1=118,f_1=8$

4. $x_1=221,f_1=45$

Q. The mean of the given data is .

$\begin{array}{cc}x& f\\ 4& 10\\ 8& 11\\ 12& 9\\ 16& 13\end{array}$

1. 10.33
2. 10
3. 10.5

Q.

The following table shows the marks obtained by 5 students in a class room, find the average marks of the classroom.

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 98& 1\\ 65& 1\\ 88& 2\\ 54& 1\end{array}$

1. 76.6

2. 77.6

3. 78.6

4. 78.9

Q.

Find the value of 'p' if the mean of the following data is 17.

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

1. 14

2. 12

3. 16

4. 18

Q.

The mean of the following distribution is:
$\begin{array}{ccccc}{\text{x}}_i& 10& 13& 16& 19\\ {\text{f}}_i& 2& 5& 7& 6\end{array}$

1. 15.2

2. 15.55

3. 15.35

4. 16

Q. Deviation = _______.

1. Class mark - assumed mean
2. Class mark - frequency
3. Class mark - upper limit
4. $\sum f_i{x}_i,\sum f_i$

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.

Find the mean of the marks obtained by 20 students in a classroom.

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 87& 2\\ 78& 3\\ 53& 1\\ 98& 2\\ 92& 2\\ 97& 1\\ 81& 2\\ 65& 2\\ 98& 3\\ 76& 2\end{array}$

1. 82.8

2. 83.8

3. 83.4

4. 81.8