Direct Method of Finding Mean

Q.

Find the missing frequencies in the following frequency distribution whose mean is 50.
$\begin{array}{ccccccc}\text{x}& 10& 30& 50& 70& 90& \text{Total}\\ \text{f}& 17& f_1& 32& f_2& 19& 120\end{array}$

Q.

The following table shows the weights of $12$ workers in a factory:

$\begin{array}{cccccc}\text{Weight (in kg)}& 60& 63& 66& 69& 72\\ \text{No. of workers}& 4& 3& 2& 2& 1\end{array}$

Find the mean weight of the workers.

Q.

Find the value of p, when the mean of the following distribution is 20.
$\begin{array}{cccccc}\text{x}& 15& 17& 19& 20+p& 23\\ \text{f}& 2& 3& 4& 5p& 6\end{array}$

Q.

Find the missing frequencies in the following frequency distribution whose mean is 34.
$\begin{array}{cccccccc}\text{x}& 10& 20& 30& 40& 50& 60& \text{Total}\\ \text{f}& 4& f_1& 8& f_2& 3& 4& 35\end{array}$

Q.

If the mean of the data is 60, find the value of p

$\begin{array}{cc}Classmark& frequency\\ 25-35& 12\\ 35-45& 16\\ 45-55& p\\ 55-65& 15\\ 65-75& 8\\ 75-85& 19\\ 85-95& 13\end{array}$

1. 17

2. 23

3. 12

4. 44

Q.

Q.

If the mean of the following data is 8, find the value of p.
$\begin{array}{ccccccc}\text{x}& 3& 5& 7& 9& 11& 13\\ \text{f}& 6& 8& 15& p& 8& 4\end{array}$

Q.

Q.

Find the vale of p for the following frequency distribution whose mean is 16.6
$\begin{array}{cccccccc}\text{x}& 8& 12& 15& p& 20& 25& 30\\ \text{f}& 12& 16& 20& 24& 16& 8& 4\end{array}$

Q.

Find the mean of the following frequency distribution:
$\begin{array}{cccccc}\text{Variables}\left(x_i\right)& 10& 30& 50& 70& 89\\ \text{Frequency}\left(f_i\right)& 7& 8& 10& 15& 10\end{array}$

Q. Question 6

A machine, on an average, manufactures 2, 825 screws a day. How many screws did it produce in the month of January 2006?

Q. The value of $\pi$ upto 50 decimal place is
3.1415926535897932384626433832795028841971693
9937510
(1) Make a frequency distribution table of digits from 0 to 9 after the decimal place.
(2) Which are the most and least occuring digits ?

Q. Question 5
Find the mean salary of 60 workers of a factory from the following table:
$$\begin{array}{cc}Salary\left(inRs\right)& Numberofworkers\\ 3000& 16\\ 4000& 12\\ 5000& 10\\ 6000& 8\\ 7000& 6\\ 8000& 4\\ 9000& 3\\ 10000& 1\\ Total& 60\end{array}$$

Q.

The following table gives the number of pages written by Sarika for completing her own book for $30$ days

Number of pages written per day $16-18,19-21,22-24,25-27,28-30$

Number of days $1,3,4,9,13$

Find the mean number of pages written per day.

Q.

The following data give the number of boys of a particular age in a class of 40 students.
$\begin{array}{ccccccc}\text{Age (in years)}& 15& 16& 17& 18& 19& 20\\ \text{Frequency}\left(f_i\right)& 3& 8& 9& 11& 6& 3\end{array}$
Calculate the mean ager of the students.

Q. Find the mean deviation about the following continuous distribution:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

Q. If the mean of the following frequency distribution is $15$, find the value of $p$.

Variable $\left(x_i\right)$	$10$	$12$	$14$	$16$	$18$
Frequency $\left(f_i\right)$	$13$	$p$	$15$	$32$	$28$

Q. If mode and median of the data is 21 and 19 , then the mean is

Q.

If the mean of the following data is 20.2, find the value of p.
$\begin{array}{cccccc}\text{Variable}\left(x_i\right)& 10& 15& 20& 25& 30\\ \text{Frequency}\left(f_i\right)& 6& 8& p& 10& 6\end{array}$

Q. The number of goals scored by a hockey team in $20$ matches is given here:
$4,6,3,2,2,4,1,5,3,0,4,5,4,5,4,0,4,3,6,4$.
Find the mean.

Q.

What is mean?

1. The simple average of the observations
2. The sum of the observations
3. The difference between any two observations
4. None of the above

Q. If the mean of $n$ observations $1^3,2^3,3^3\cdots n^{3}is\frac{7{(n+1)}^2}{4},$ then the value of $n$ equals

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

Q.

What is the mean of the following numbers: 2, 6, 4, 9, 7, 3, 5, 4, 3, 7.

1. 4

2. 4.8

3. 5

4. 5.6

Q. The average temperature for the the first 5 day of the year is ${40}^{\circ }$ and the average temperature from second to sixth day is ${42}^{\circ }$ and the ratio between the temperature of $1^{st}$ day and the $6^{th}$ day is $3:4$, find the temperature of the sixth day.

Q.

What is mean?

1. The sum of the observations

2. The simple average of the observations

3. The difference between any two observations

4. None of the above

Q. The following table gives the weekly wages (in Rs.) of workers in a factory:

Weekly wages (in Rs.)	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$	$75-80$	$80-85$	$85-90$
No. of workers	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

Calculate the number of workers getting weekly wages below $Rs.80$.

Q. A person made 165 telephone calls in the month of May in a year It was Friday on 1st May of the year The average of telephone calls on Sundays of the months was 7 What was the average of the telephone calls per day on the rest days of the months

1. $\frac{165}{31}$
2. $5$
3. $7$
4. $\frac{137}{27}$

Q. The mean of the following frequency distributed of $200$ observation is $332$. Find the value of $x$ and $y$

Class	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$	$350-400$	$400-450$	$400-450$	$500-550$
Frequency	$4$	$8$	$x$	$42$	$50$	$y$	$32$	$6$	$4$

Q. If the mean of 100 observations is 50, then the sum of all the observations is ____.

1. 5000
2. 5260
3. 5050
4. 5105

Q. The mean of the following frequency distribution is $62.8$ and the sum of the observation is $50$. Find the missing frequencies $F_1$ and $F_2$.

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120	Total
Frequency	5	$F_1$	10	$F_2$	7	8	50