Mean of Ungrouped Frequency Distribution by Deviation Method

Q.

Question 8
The mean of the following frequency distribution is 50 but the frequencies $f_1$ and $f_2$ in classes 20-40 and 60-80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.
$\begin{array}{cccccc}Class& 0-20& 20-40& 40-60& 60-80& 80-100\\ Frequency& 17& f_1& 32& f_2& 19\end{array}$

Q. Actual Mean = + Distributed Mean

1. Mean
2. Assumed Mean
3. Arithmetic mean

Q. Obtain the mean of the given data by assumed mean method. $x_i$ $f_i$

25	3
35	5
45	4
55	6
65	8
75	10
85	9

1. 66.11
2. 55.22
3. 50.14
4. 62.14

Q. Find the mean salary of $60$ workers of a factory from the following table:

Q. If $\overline{x}$ is the mean of $x_1,x_2,...,x_n,$ then for $a\ne 0$, the mean of $a{x}_{1,}a{x}_2,...,a{x}_n,\frac{x_1}{a},\frac{x_2}{a},...,\frac{x_n}{a}$ is
(a) $\left(a+\frac{1}{a}\right)\overline{x}$

(b) $\left(a+\frac{1}{a}\right)\frac{\overline{x}}{2}$

(c) $\left(a+\frac{1}{a}\right)\frac{\overline{x}}{n}$

(d) $\frac{\left(a+{\displaystyle \frac{1}{a}}\right)\overline{x}}{2n}$

Q. Find the mean of the following frequency distribution using assumed mean method:

1. 17.7
2. 18.8
3. 19
4. 19.9

Q. In the table given below, Find the mean.
(i)

Class mark	Frequency
5	3
15	9
25	15
35	13

Q.

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

1. False

2. True

Q. The following data give the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students by assumed mean method.
Age (in years) Number of students

13	3
14	8
15	9
16	11
17	6
18	3

1. 17.25
2. 16.55
3. 15.45
4. 18.35

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. 0.098
2. 0.122
3. 0.096
4. 0.1

Q. Mean of a set of observations is the value which

1. occurs most frequently
2. divides observations into two equal parts
3. is a representative of whole group
4. is the sum of observations