Assumed Mean Method of Finding Mean

Q. Express each number as a product of its prime factors:

Q.

Find the mean of the following data, using assumed-mean method:
$\begin{array}{ccccccc}\text{Class}& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ \text{Frequency}& 20& 35& 52& 44& 38& 31\end{array}$

Q. If the mean of the following frequency distribution is 18 , find the missing frequency .

Class interval : 11-13 13-15 15-17 17-19 19-21 21-23 23-25

Frequency: 3 6 9 13 f 5 4

Q. For what value of k will the consecutive terms 2K+1, 3K+3 and 5k-1 form an A. P?

Q.

Question 3
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

$\begin{array}{cc}\text{Expenditure (in Rs)}& \text{Number of families}\\ 1000-1500& 24\\ 1500-2000& 40\\ 2000-2500& 33\\ 2500-3000& 28\\ 3000-3500& 30\\ 3500-4000& 22\\ 4000-4500& 16\\ 4500-5000& 7\end{array}$

Q.

Question 4
The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

$\begin{array}{cc}\text{Number of students per teacher}& \text{Number of states/U.T}\\ 15-20& 3\\ 20-25& 8\\ 25-30& 9\\ 30-35& 10\\ 35-40& 3\\ 40-45& 0\\ 45-50& 0\\ 50-55& 2\end{array}$

Q.

Find the mean marks per student, using assumed-mean method:
$\begin{array}{ccccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of students}& 12& 18& 27& 20& 17& 6\end{array}$

Q.

Find the class marks of classes $10-25$ and $35-55$

Q.

The following table gives the lifetime in days of $100$ electricity tubes of a certain make:

Find the mean lifetime of electricity tubes by the step deviation method.

1. $145$

2. $100$

3. $60$

4. $175$

Q.

The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.

1. 36

2. 34

3. 22

4. 33

Q. Question 1
Find the mean marks of students for the following distribution
$\begin{array}{cc}Marks& Numberofstudents\\ 0andabove& 80\\ 10andabove& 77\\ 20andabove& 72\\ 30andabove& 65\\ 40andabove& 55\\ 50andabove& 43\\ 60andabove& 28\\ 70andabove& 16\\ 80andabove& 10\\ 90andabove& 8\\ 100andabove& 0\end{array}$

Q. The arithmetic mean of the following data is 25, find the value of k.

xi:	5	15	25	35	45
fi:	3	k	3	6	2

Q. Question 5
The daily income of a sample of 50 employee are tabulated as follows.
$\begin{array}{ccccc}\text{Income(in~Rs)}& 1-200& 201-400& 401-600& 601-800\\ \text{Number of employees}& 14& 15& 14& 7\end{array}$
Find the mean daily income of employees.

Q.

To find out the concentration of $S{O}_2$ in the air (in parts per million, i.e., ppm) , the data was collected for $30$ localities in a certain city and is presented below. Find the mean concentration of $S{O}_2$ in the air.

Concentration of SO2 ( in ppm)	Frequency
0.00 – 0.04	4
0.04 – 0.08	9
0.08 – 0.12	9
0.12 – 0.16	2
0.16 – 0.20	4
0.20 – 0.24	2

Q.

The table below shows the daily expenditure on food of 30 households in a locality:
$\begin{array}{cc}\text{Daily expenditure (in Rs.)}& \text{Number of households}\\ 100-150& 6\\ 150-200& 7\\ 200-250& 12\\ 250-300& 3\\ 300-350& 2\end{array}$
Find:

(a) mean of daily expenditure on food.

(b) median of daily expenditure on food.

Q.

What is the symbol for the sample standard deviation?

Q.

Find the mean of the following data, using assumed-mean method:
$\begin{array}{cccccc}\text{Marks}& 100-120& 120-140& 140-160& 160-180& 180-200\\ \text{Number of students}& 10& 20& 30& 15& 5\end{array}$

Q.

Question 3
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

$\begin{array}{cccccccc}\text{Daily pocket allowance (in Rs)}& 11-13& 13-15& 15-17& 17-19& 19-21& 21-23& 23-25\\ \text{Number of workers}& 7& 6& 9& 13& f& 5& 4\end{array}$

Q.

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.
$\begin{array}{cccc}\text{Expenditure}& \text{Frequency}& \text{Expenditure}& \text{Frequency}\\ \left(\text{in rupees}\right)\left(x_i\right)& \left(f_i\right)& \left(\text{in rupees}\right)\left(x_i\right)& \left(f_i\right)\\ 100-150& 24& 300-350& 30\\ 150-200& 40& 350-400& 22\\ 200-250& 33& 400-450& 16\\ 250-300& 28& 450-500& 7\end{array}$
Find the average expenditure (in rupees) per household.

Q. If the mean of the following distribution is 2.6, then the value of y is

Variable (x):	1	2	3	4	5
Frequency	4	5	y	1	2

(a) 3
(b) 8
(c) 13
(d) 24

Q.

Calculate the mean of the following distribution:
$\begin{array}{cc}ClassInterval& Frequency\\ 0-10& 8\\ 10-20& 5\\ 20-30& 12\\ 30-40& 35\\ 40-50& 24\\ 50-60& 16\end{array}$

Q.

Find the harmonic mean of the given numbers

$\frac{1}{2},\frac{1}{4},\frac{1}{6}$

1. $\frac{36}{11}$

2. $\frac{1}{4}$

3. $\frac{21}{36}$

4. $\frac{4}{1}$

Q.

Mean of $6$ observations is $10$ and their variance is $\frac{20}{3}$. If their observations are $15,11,10,7,a,b$ then $\left|a-b\right|$ is equal to:

1. $2$

2. $1$

3. $3$

4. $4$

Q.

Find the value of $f$ if the mean of the following distribution is $25.2$.

Class-interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$8$	$12$	$f$	$11$	$9$

Q.

While calculating the mean of a given data by the assumed-mean method, the following values were obtained:

A=25, $\sum f_i{d}_i=110,\sum f_i=50.$

Find the mean.

Q.

Calculate the mean of the distribution given below using the short cut method
$\begin{array}{cccccccc}Marks& 11-20& 21-30& 31-40& 41-50& 51-60& 61-70& 71-80\\ No.ofstudents& 2& 6& 10& 12& 9& 7& 4\end{array}$

Q. For the month of February, a class teacher of Class IX has the following absentee record for 45 students. Find the mean number of days, a student was absent.
$\begin{array}{ccccccc}\text{Number of days of absent}& 0-4& 4-8& 8-12& 12-16& 16-20& 20-24\\ \text{Number of students}& 18& 3& 6& 2& 0& 1\end{array}$

Q.

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
$\begin{array}{cc}\text{Literacy rate (in \%)}& \text{No. of cities}\\ 45-55& 3\\ 55-65& 10\\ 65-75& 11\\ 75-85& 8\\ 85-95& 3\end{array}$

1. 66.44

2. 69.43

3. 67.39

4. 71.55

Q.

A student scores $56$ on a geography test and $246$ on a mathematics test. The geography test has a mean of $80$ and a standard deviation of $20$. The mathematics test has a mean of $300$ and a standard deviation of $36$. If the data for both tests are normally distributed, on which test did the student score better?

Q.

Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method.

$\begin{array}{cccccc}NumberofMangoes& 50-52& 53-55& 56-58& 59-61& 62-64\\ Numberofboxes& 15& 110& 135& 115& 25\end{array}$

Can the assumed mean be 60?

1. 53.87, yes
2. 59.95, no
3. 57.18, yes
4. 54.99, no