Mean of Continuous Series

Q.

Calculate arithmetic mean from the following data:

$\begin{array}{cccccc}\text{Marks}& 0-10& 10-20& 20-40& 40-70& 70-100\\ \text{No. of Students}& 8& 12& 30& 6& 4\end{array}$

Q. Find the mean age in years from the frequency distribution given below:
$\begin{array}{cc}Classintervalof& Frequency\\ ageinyears& \left(f_i\right)\\ 25-29& 4\\ 30-35& 14\\ 35-39& 22\\ 40-45& 16\\ 45-49& 6\\ 50-55& 5\\ 55-59& 3\\ Total& 70\end{array}$

1. 39.39
2. 39.35
3. 40.15
4. 40.39

Q. Find the mean of the step deviations:
$\begin{array}{ccccc}Class& Frequency& Classmark& d_i& u_i=\frac{d_i}{h}\\ interval& \left(f_i\right)& \left(x_i\right)& (x_i-a)& \\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

1. $0$
2. $\frac{1}{188}$
3. $250$
4. $250.52$

Q.

Find the mean employee age from the table below. Use assumed mean method.

$\begin{array}{cc}Age\left(inyears\right)& Numberofemployees\\ 20-25& 20\\ 25-30& 15\\ 30-35& 12\\ 35-40& 10\\ 40-45& 10\\ 45-50& 8\end{array}$

1. 29. 67

2. 30.75

3. 32.43

4. 36.83

Q. The following table shows marks secured by 140 students in an examination:

$\begin{array}{cc}Marks& Numberofstudents\\ 0-10& 20\\ 10-20& 24\\ 20-30& 40\\ 30-40& 36\\ 40-50& 20\end{array}$

Calculate mean marks by the step deviation method.

1. 25
2. 25.86
3. 26.92
4. 20.4

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

Find $\sum f_i{x}_i$ from the given table.

1. 434
2. 208
3. 444
4. Data inadequate

Q. Look at the following table below.
$\begin{array}{cc}Classinterval& Classmark\\ 0-5& --\\ 5-10& --\\ 10-15& \\ 15-20& \end{array}$

Fill in the blanks with the class marks of the corresponding class intervals.

1. 5, 10
2. 3, 8
3. 0, 5
4. 2.5, 7.5

Q.

For calculating the mean of grouped data, the mid point of each class interval is chosen to represent all the observations from that class.

1. True

2. False

Q. Calculate the mean of the following data.

$\begin{array}{cc}Class& Frequency\\ 0-100& 16\\ 100-200& 11\\ 200-300& 7\\ 300-400& 10\\ 400-500& 6\end{array}$

1. 235
2. 198
3. 208
4. 226

Q.

Class mark of a class is __________

1. Upper limit + lower limit

2. 

3. 

4. upper limit - lower limit

Q.

The class mark for a class interval while calculating the mean is its upper limit.

1. False

2. True