Assumed Mean Method

Q. In the formula $\overline{\mathrm{X}}=\mathrm{a}+\frac{\mathrm{\Sigma }{\mathrm{f}}_{\mathrm{i}}{\mathrm{d}}_{\mathrm{i}}}{\mathrm{\Sigma }{\mathrm{f}}_{\mathrm{i}}}$, for finding the mean of grouped data ${d_i}^{{}^s}$ are derivations from $a$ of
(a) lower limits of classes (b) upper limits ofclasses
(c) mid-points of classes (d) frequency of the class marks

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

Q.

In the assumed mean method, if A is the assumed mean, then deviation $d_i$ is :

1. 
2. 
3. 
4. 

Q.

The following table gives the marks scored by students in an exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Above}0& 80\\ \text{Above}10& 77\\ \text{Above}20& 72\\ \text{Above}30& 65\\ \text{Above}40& 55\\ \text{Above}50& 43\\ \text{Above}60& 23\\ \text{Above}70& 16\\ \text{Above}80& 10\\ \text{Above}90& 8\\ \text{Above}100& 0\end{array}$

Find the mean for the following data using assumed mean method.

1. 51.25
2. 50
3. 30
4. 35

Q. Calculate the arithmetic mean using Assumed mean method.

1. $62.5$ rupees
2. $61.5$ rupees
3. $64.5$ rupees
4. $65.5$ rupees

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?

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

1. 59.95

2. 57.18

3. 54.99

4. 53.87

Q.

The age of the employees in a startup company is shown below. Find the average age of the employees.

$\begin{array}{cc}\text{Age}& \text{No. of Employees}\\ 18-26& 30\\ 26-34& 70\\ 34-42& 50\\ 42-50& 30\\ 50-58& 10\\ 58-66& 10\end{array}$ [3 MARKS]

Q.

Consider the following distribution of SO2 concentration in the air(in ppm = parts per million) in 30 localities. Find the mean SO2 concentration using assumed mean method. Also find the values of A, B and C

$$\begin{array}{cccc}ClassInterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a\\ 0.00-0.04& 4& 0.02& -0.08\\ 0.04-0.08& 9& 0.06& A.........\\ 0.08-0.12& 9& 0.10& B........\\ 0.12-0.16& 2& 0.14& 0.04\\ 0.16-0.20& 4& 0.18& C........\\ 0.20-0.24& 2& 0.22& 0.12\\ Total& \sum f_i=30& & \end{array}$$

1. -0.04, 0, 0.04, 0.098

2. -0.04, 0, 0.04, 0.2

3. -0.04, 0, 0.04, 0.6

4. -0.04, 0, 0.04, 0.5

Q.

Standard deviation about mean $\overline{x}$ for a given discrete frequency distribution x₁, x₂, x₃, ....x_n with frequencies f₁, f₂, f₃, .... f_n is.

Q.

What mean standard deviation?

Q.

Consider a grouped data distribution for which the mean is found by assumed mean method.

P = sum of the products of ‘d’ and frequency for each class interval

Here $d_i=x_i-A$

Q = total number of observations

A = assumed mean

M = mean of given grouped data distribution

Which of the following statements is true?

1. $M=A+\frac{Q}{P}$
2. $M=A+\frac{P}{Q}$
3. $M=Q+\frac{A}{P}$
4. $M=P+\frac{A}{Q}$

Q. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is ___.

Q. The class mark of the class with maximum frequency is taken as the ______.

1. assumed mean
2. mean
3. direct mean
4. harmonic mean

Q.

Calculate the Mean of the given distribution, using Assumed mean Method.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 10-20& 2\\ 20-30& 6\\ 30-40& 10\\ 40-50& 12\\ 50-60& 9\\ 60-70& 8\\ 70-80& 4\\ 80-90& 3\end{array}$

1. 48.89

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:

Concentration of $S{O}_2$ (in ppm)	Frequency
$0.00-0.04$	$4$
$0.04-0.08$	$9$
$0.08-0.12$	$9$
$0.12-0.16$	$2$
$0.16-0.20$	$4$
$0.20-0.24$	$2$

Find the mean concentration of $S{O}_2$ in the air.

Q.

How is deviation calculated?

Q. The following frequency distribution showing the marks obtained by $25$ students in science subject. Find the mean using Assumed mean method.

1. $90$
2. $91$
3. $92$
4. $93$

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:

Concentration of $S{O}_2$ (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

Find the mean concentration of $S{O}_2$ in the air.

1. 0.099
2. 0.089
3. 0.09
4. 0.99

Q. Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is

1. $\frac{(n+1)d}{(2n+1)}$
2. $\frac{(nd}{(2n+1)}$
3. $\frac{n(n+1)d}{(2n+1)}$
4. $\frac{2(n+1)d}{n(n+1)}$

Q.

The marks obtained by the students of a class , in a exam which was out of 50 mark given below

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$

(i) Find the mean for the ungrouped data.

(ii) Represent the same data as grouped data, with class interval of width = 10

Q. {1, 4, 5, 7, 8} - Find the value of mean deviation.

1. 2
2. 4
3. 5
4. 6

Q. Question 4
In the formula $\overline{x}=a+h\left(\frac{\sum f_i{u}_i}{\sum f_i}\right),$ for finding the mean of grouped frequency distribution $u_i$ is equal to
(a) $\frac{x_i+a}{h}$
(b) $x_i+a$
(c) $\frac{x_i+a}{h}$
(a) $\frac{a-x_i}{h}$

Q.

Suppose a population A has 100 observations 101, 102, . . . . 200 and another population B has 100 observations 151, 152, . . . . 250. If $V_A$ and $V_B$ represent the variances of the two populations, respectively then $\frac{V_A}{V_B}$ is

1. 1

2. $\frac{9}{4}$

3. $\frac{4}{9}$

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

Q.

The following table gives the marks scored by students in an exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Above}0& 80\\ \text{Above}10& 77\\ \text{Above}20& 72\\ \text{Above}30& 65\\ \text{Above}40& 55\\ \text{Above}50& 43\\ \text{Above}60& 23\\ \text{Above}70& 16\\ \text{Above}80& 10\\ \text{Above}90& 8\\ \text{Above}100& 0\end{array}$

Find the mean for the following data using assumed mean method. [4 MARKS]

Q.

In the formula $\overline{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$ , the "a" stands for assumed mean.

1. True

2. False

Q.

The following table gives the marks scored by students in an exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Above}0& 80\\ \text{Above}10& 77\\ \text{Above}20& 72\\ \text{Above}30& 65\\ \text{Above}40& 55\\ \text{Above}50& 43\\ \text{Above}60& 23\\ \text{Above}70& 16\\ \text{Above}80& 10\\ \text{Above}90& 8\\ \text{Above}100& 0\end{array}$

Find the mean for the following data using assumed mean method.

Q.

Given below is the concentration of SO₂ in air(in ppm = parts per million) in 30 localities:
$\begin{array}{cc}S{O}_2\text{concentration (in ppm)}& \text{Number of localities}\\ 0.00-0.04& 4\\ 0.04-0.08& 9\\ 0.08-0.12& 9\\ 0.12-0.16& 2\\ 0.16-0.20& 4\\ 0.20-0.24& 2\end{array}$
Find the mean of $S{O}_2$ concentration using assumed - mean method.

1. 0.1

2. 0.123

3. 0.144

4. 0.16

Q. While computing mean of grouped data, we assume that the frequencies are:

1. evenly distributed over all the class
2. centred at the classmarks of the class
3. centred at the upper limits of the class
4. centred at the lower limits of the class

Q. Given below is the concentration of SO₂ in air(in ppm = parts per million) in 30 localities:
$\begin{array}{cc}S{O}_2\text{concentration (in ppm)}& \text{Number of localities}\\ 0.00-0.04& 4\\ 0.04-0.08& 9\\ 0.08-0.12& 9\\ 0.12-0.16& 2\\ 0.16-0.20& 4\\ 0.20-0.24& 2\end{array}$
Find the mean of $S{O}_2$ concentration using assumed - mean method.

1. 0.1
2. 0.098
3. 0.122
4. 0.096

Q. In the assumed mean method, if A is the assumed mean, then deviation $d_i$ is :

1. 
2. 
3. 
4.