Finding Mean for Grouped Data When Class Intervals Are Not Given

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

Q.

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

1. 15.55

2. 16

3. 15.2

4. 15.35

Q.

$$\begin{array}{ccc}{x}_i& f_i& f_i{x}_i\\ 4& 10& ........\\ 8& 11& ........\\ 12& 9& .........\\ 16& 13& .........\\ & & \sum f_i{x}_i=..........\end{array}$$

Find the value of $\sum f_i{x}_i$.

1. 40
2. 88
3. 444
4. 208

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.

The average weight of a group of 25 men was calculated to be 78.4 kg. It was discovered later that one weight was wrongly entered as 69 kg instead of 96 kg. What is the correct average ?

1. 79.48

2. 77.56

3. 80.30

4. 75.76

Q.

$\sum$fx = 5x + 2, $\sum$f = 12. If the mean of the distribution is 6, what is the value of x?

1. 12

2. 15

3. 14

4. 18

Q.

The mean of first 10 natural numbers is ______.

1. 5.5

2. 6.5

3. 5

4. 4.5

Q.

Which of the following is the mean of a set of observations?

1. Sum of the values of all the observations divided by the total number of observations

2. Sum of the values of all the observations divided by twice the total number of observations

3. The most common datum in a data set

4. The most important datum in a data set

Q.

The Mean of the first 10 prime numbers is__

Q.

What is the mean of the given data?

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

1. 11.1
2. 25
3. 44
4. 10.3