Mean of Ungrouped Frequency Distribution by Simple Method

Q. Find the mean of the following data?

1. 25
2. 40
3. 35
4. 30

Q.

The mean of a data is defined as______

Q.

Let $x,y,z$ be three observations. The mean of these observations is:

1. $\frac{\left(x\times y\times z\right)}{3}$

2. $\frac{\left(x+y+z\right)}{3}$

3. $\frac{\left(x-y-z\right)}{3}$

4. $\frac{\left(x\times y+z\right)}{3}$

Q.

Michael appeared in an examination and obtained the following marks out of 100.

$$\begin{array}{cc}\text{Name}& \text{Michael}\\ \text{Physics}& 87\\ \text{Chemistry}& 82\\ \text{Biology}& 82\\ \text{Mathematics}& 98\end{array}$$

Measure the central tendency of the above data.

1. Mean = 87.25, Median = 84.5 and Mode = 82

2. Mean = 86.25, Median = 82 and Mode = 98

3. Mean = 87.25, Median = 81 and Mode= 87

4. Mean= 87.25, Median = 87 and Mode = 82

Q. Define mean?

Q.

The mean of 15 observations is 8. If the mean of the values of first eight observations is 7 and that of the values of last eight observations is 10, then what is the value of the 8th observation?

1. 8
2. 16
3. 10
4. 12

Q.

The distribution of the heights 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. If each value of the data is increased by 5, their mean:

1. will become 5 times its original mean.
2. will be decreased by 5
3. will be increased by 5
4. remains the same

Q. The marks obtained by 40 students in a class are presented in the form of a table. Find the mean marks 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. 26.44
4. 29.91

Q. If $\overline{X_1}$ and $\overline{X_2}$ are the means of two distributions such that $\overline{X_1}<\overline{X_2}$ and $\overline{X}$ is the mean of combined distribution, then

1. $\overline{X}<\overline{X_1}$
2. $\overline{X}>\overline{X_2}$
3. $\overline{X}=\frac{\overline{X_1}-\overline{X_2}}{2}$
4. $\overline{X_1}<\overline{X}<\overline{X_2}$

Q. Find the mean of the marks obtained by 30 students in a school test, marks are 10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88,
80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60 and 88.

1. 59.2
2. 58
3. 57.3
4. 59.3

Q. The mean of 15 observations is 8. If the mean of the values of first eight observations is 7 and that of the values of last eight observations is 10, then what is the value of the 8th observation?

Q. If $25$ is the arithmetic mean of $X$ and $46,$ then find $X.$

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

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 monthly salary of 10 members of a group is ₹ 1445, one more member whose monthly salary is ₹ 1500 joins the group. Find the mean monthly salary of 11 members of the group.

1. 1400
2. ₹1460
3. ₹1480
4. ₹1450

Q.

The mean marks of 100 students were found to be 40. Later on, it was discovered that a score of 53 was misread as 83. Then, what will be the correct Mean?

1. 37.5
2. 35.6
3. 39.7
4. 38.7

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. 77.6

2. 78.6

3. 78.9

4. 76.6

Q. What is the mean of the given data?

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

1. 10.33
2. 10
3. 43
4. 444

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. 15.55

2. 16

3. 15.2

4. 15.35