Assumed Mean Method of Finding Mean

Q.

For finding mean by assumed mean method

$\overline{x}$ = a + $\frac{(\sum f\times d)}{\sum f}$

Where d and a are respectively

1. Assumed frequency , difference between class mark and assumed mean

2. Difference between class mark and assumed mean, assumed frequency

3. Difference between class mark and assumed frequency , assumed mean

4. Difference between class mark and assumed mean , assumed mean

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. 0.122

3. 0.144

4. 0.16

Q. Deviation = _______.

1. Class mark - assumed mean
2. Class mark - frequency
3. Class mark - upper limit
4. $\sum f_i{x}_i,\sum f_i$

Q.

There is a grouped data distribution for which mean is to be found by step deviation method.

$$\begin{array}{ccccc}ClassInterval& NumberofFrequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& D......\\ 100-200& 39& 150& B.....& E.....\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& C.....& F......\\ Total& A=\sum f_i=......& & & \end{array}$$

Find the value of A, B, C, D, E and F respectively.

1. 188 , -100, 200, -2 , -1 and 2

2. 186 , 100, -200, -2 , -1 and 2

3. 188 , 100, -200, 2 , -1 and -2

4. 186 , -100, -200, -2 , -1 and 2

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. 53.87

3. 57.18

4. 54.99

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

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

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

1. 
2. 
3. 
4. 

Q.

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

1. False

2. True

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