Mean for Frequency Distribution Table

Q.

Find the mean salary of 60 workers of a factory from the following table:
$$\begin{array}{cc}Salary\left(in₹\right)& Numberofworkers\\ 3000& 16\\ 4000& 12\\ 5000& 10\\ 6000& 8\\ 7000& 6\\ 8000& 4\\ 9000& 3\\ 10000& 1\\ Total& 60\end{array}$$

1. ₹ 4873.51

2. ₹ 5083.33

3. ₹ 5099.25

4. ₹ 4902.5

Q.

Find the missing frequency p in the following frequency distribution whose mean is 28.25
$\begin{array}{ccccccc}\text{x}& 15& 20& 25& 30& 35& 40\\ \text{f}& 8& 7& p& 14& 15& 6\end{array}$

1. 12

2. 15

3. 10

4. 2

Q.

Find the missing value of p for the following distribution whose mean is 12.58.

$\begin{array}{cccccccc}x:& 5& 8& 10& 12& p& 20& 25\\ f:& 2& 5& 8& 22& 7& 4& 2\end{array}$

1. 14

2. 15

3. 12

4. 16

Q. A number 75 is misread as 57. Find the reading error percentage.

1. 32%
2. 33%
3. 27%
4. 24%

Q.

Question 3(d)

Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.

$\frac{q}{2}=7(7,2,10,14)$

Q.

Find the mean of the following data:

$\begin{array}{cccccccc}x:& 19& 21& 23& 25& 27& 29& 31\\ f:& 13& 15& 16& 18& 16& 15& 13\end{array}$

1. 10

2. 32

3. 25

4. 17

Q.

Absolute error of a number is 5 and Relative error for same number is 0.2. Then the actual value of number is

1. 50

2. 1

3. 25

4. 0.04

Q. The average of 5 and 8 is ____ .

1. 6
2. 7
3. 6.5
4. any number between 6 and 7

Q. Average of the first six even natural numbers is:

1. $7$
2. $5$
3. $3$
4. $1$

Q. What is Arithmetic Mean and Geometric Mean

Q.

Express 3460 grams in kilograms.

Now express $17\frac{1}{2}$ kg in grams. [2 MARKS]

Q.

The daily expenditure of $100$ families are given below. Calculate $f_1$and $f_2$ if the mean daily expenditure is $Rs188$.

Expenditure in Rs.	$140-160$	$160-180$	$180-200$	$200-220$	$220-240$
No. of families	$5$	$25$	$f_1$	$f_2$	$5$

Q. Find the median class for the given distribution:
$\begin{array}{cccccc}Weeklywages\left(₹\right)& 0-100& 100-200& 200-300& 300-400& 400-500\\ No.ofworkers& 40& 39& 34& 30& 45\end{array}$

1. 100-200
2. 400-500
3. 200-300
4. 300-400

Q.

The A.M. of the first ten odd numbers is -

1. $10$

2. $100$

3. $1000$

4. $1$

Q. Find the arithmetic mean of first ten odd natural numbers.

Q. Question 17
If $\overline{x_1},\overline{x_2},\overline{x_3},\dots \dots \overline{x_n}$, are the means of n groups with $n_1,n_2,n_n$ number of observations, respectively. Then the mean $\overline{x}$ of all the groups:

A) ${\sum }_{i=1}^n{n}_i\overline{x_i}$
B) $\frac{{\sum }_{i=1}^n{n}_i\overline{x_i}}{n^2}$
C) $\frac{{\sum }_{i=1}^n{n}_i\overline{x_i}}{{\sum }_{i=1}^n{n}_i}$
D) $\frac{{\sum }^n{n}_i\overline{x_i}}{2n}$

Q.

An average daily wage of 10 workers in a factory A is Rs. 30 and an average daily wage of 20 workers in a factory B is Rs. 15. Find the average daily wages of all workers of both the factories.

Q. Find the mean of the first ten natural numbers.

Q. An average daily wages of $10$ workers in a factory '$A$' is Rs. $30$ and an average daily wages of $20$ workers in a factory '$B$' is Rs. $15$. Find the average daily wages of all workers of both the factories.

1. $20$
2. $40$
3. $10$
4. $15$

Q. Let set $M=\{x,2x,4x\}$ for any number $x$. If the average (arithmetic mean) of the numbers in set $M$ is $14$, find the value of $x$.

1. $10$
2. $6$
3. $7$
4. $2$
5. $12$

Q. What is the arithmetic mean of the squares of first five natural numbers?

1. $9$
2. $11$
3. $13$
4. $15$

Q.

The mean of the following distribution is:

$\begin{array}{cccccc}x:& 10& 12& 20& 25& 35\\ f:& 3& 10& 15& 7& 5\end{array}$

1. 42

2. 22

3. 40

4. 20

Q. Write any two merits of arithmetic mean.

Q. Find the mean of the following $20$ observations:
$12,2,3,3,2,12,12,1,4,5,4,4,3,11,11,2,6,2,3,6,12$.

1. $4$
2. $6$
3. $5$
4. $7$

Q. Write two demerits of arithmetic mean.

Q. If the mean of $5$ equations $x,x+2,x+3,x+4,x+6$ is $4$, find the value of $x$ ?

Q. The mean of $7,9,x+3,12,2x-1$ and $3$ is $9$. Find the value of $x$

Q. The heights of $10$ students were measured in cm and the results are as follows :
$147,139,135,136,149,166,152,163,155,144$
(i) What is the range of the data?
(ii) What is the mean height of the students?
(iii) How many students are there whose height is more than the mean height?

1. $30$; $100.5$; $3$
2. $31$; $148.6$; $5$
3. $32$; $149$; $5$
4. $28$; $148.6$; $4$

Q. If the mean of $10,12,18,13,x,17$ is $15$, find ${}^{\prime }{x}^{\prime }$.

Q. The mean of all the factors of $12$ is:

1. $3\frac{2}{3}$
2. $4\frac{3}{2}$
3. $4\frac{2}{3}$
4. $12$