Mean

Q.

The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12, 14, find the remaining two observations.

Q.

The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

1. 80

2. 40

3. 20

4. 60

Q.

Ravi obtained 70 and 75 marks in first two unit tests. Find the minimum marks he should get in the third test to have on average of at least 60 marks.

Q.

The mean and variance of $8$ observations are $10$ and $13.5$, respectively. If $6$ of these observations are $5,7,10,12,14,15$ then the absolute difference of the remaining two observations is:

1. $3$

2. $9$

3. $7$

4. $5$

Q. 22. In a binomial distribution, the mean is 4 and variance is 3. Then find its mode.

Q.

Consider a set of $3n$ numbers having variance $4$. In this set, the mean of the first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3$. A new set is constructed by adding $1$ into each of the first $2n$ numbers and subtracting $1$ from each of the remaining n numbers. If the variance of the new set is $k$, then $9k$ is equal to

Q.

To receive Grade 'A' in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get Grade 'A' in the course.

Q. The mean of a set of numbers is $\overline{x}$ If each number is multiplied by $\lambda$ , then the mean of new set is

1. 
2. 
3. None of these
4. 

Q. An automobile driver travels from plane to a hill station 120 km distant at an average speed of 30 km per hour. He than makes the return trip at an average speed of 25 km per hour. He covers another 120 km distance on plane at an average speed of 50 km per hour. His average speed over the entire distance of 360 km will be

1. 
2. 
3. None of these
4. 

Q. There are 70 boys and 30 girls in a class. The average score of boys is 75. The average score of 100 students is 72. The average score of girls is .

1. 73
2. 65
3. 62
4. 74

Q. The mean of first three terms is 14 and mean of next two terms is 18. The mean of all the five terms is

1. 15
2. 15.6
3. 15.2
4. 14.5

Q. In a class of $5$ students, average weight of the $4$ lightest students is $40$ kg, average weight of the $4$ heaviest students is $45$ kg. Then the difference between the maximum and minimum possible average weight is

1. $2$
2. $3$
3. $1.5$
4. $2.5$

Q. The average of n numbers $x_1,x_2,x_3,..........,x_n$ is M. If $x_n$ is replaced by x’, then new average is

1. $M-x_n+x^{!}$
2. $\frac{nM-x_n+x^{!}}{n}$
3. $\frac{(n-1)M+x^{!}}{n}$
4. $\frac{M-x_n+x^{!}}{n}$

Q.

The A.M. of a set of 50 numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the A.M. of the remaining set of numbers is

1. 36

2. 36.5

3. 37.5

4. 38.5

Q. The mean marks got by $300$ students in the subject of statistics was $45$. The mean of top $100$ of them was found to be $70$ and the mean of last $100$ was known to be $20$, then the mean of remaining $100$ students is

Q.

For the following data, mean of x is found to be 7.3. The missing frequency is
x : 5 6 7 8 9
f : 4 6 12 - 8

1. 10

2. 9

3. 8

4. 7

Q. For the given data,
$\begin{array}{ccccccc}\text{Weight (in kg)}& 20& 24& 25& 30& 32& 35\\ \text{Number of students}& 2& 1& 3& 1& 2& 1\end{array}$
the correct option(s) is/are

1. mean is $27$
2. median is $25$
3. mode is $21.4$
4. median is $26$

Q. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: Firm A Firm B No. of wage earners 586 648 Mean of monthly wages Rs 5253 Rs 5253 Variance of the distribution of wages 100 121 (i) Which firm A or B pays larger amount as monthly wages? (ii) Which firm, A or B, shows greater variability in individual wages?

Q.

The average weight of 35 students in a class is 40kg. If the weight of the teacher is also included, the average rises by 0.5 kg. The weight of the teacher is

1. 40.5 kg

2. 50 kg

3. 58 kg

4. 64 kg

Q. The weighted mean of the first n natural numbers whose weights are equal to the corresponding numbers is

1. $2n+1$
2. $\frac{n+1}{2}$
3. $\frac{2n+1}{3}$
4. $\frac{(n+1)(2n+1)}{6}$

Q. If the mean of numbers $28,x,42,78$ and $104$ is $62,$ then the mean of $48,62,98,124$ and $x$ is

Q. Median of the data 10 21, 5, 6, 4, 12, 14, 3, is(1) 16(3) 4(2) 8(4) None of these

Q. The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by $\frac{1}{2}$ kg, the weight of the teacher is

1. 40.5 kg
2. 50 kg
3. 41 kg
4. 58 kg

Q. 44. The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.

Q. The mean of following frequency table is $50.$
If the total of frequency is $120.$ Then the missing frequencies $f_1,f_2$ are respectively
$\begin{array}{cccccc}\text{Class}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Frequency}& 17& f_1& 32& f_2& 19\end{array}$

1. $24,28$
2. $28,24$
3. $25,27$
4. $27,25$

Q. In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls

1. 65
2. 73
3. 68
4. 74

Q. The average weight of the students of a class is $60kg$. If eight new students of average weight $64kg$ join the class, the average weight of the entire class becomes $62kg$. How many students were there in the class initially?

1. $8$
2. $24$
3. $16$
4. $12$

Q. The mean weight of $150$ students in a certain class is $60$kg. The mean weight of boys in the class is $70$kg and that of girls is $55$kg, then number of boys and girls respectively are

1. $100,50$
2. $50,100$
3. $75,75$
4. $60,90$

Q. f the mean of 15 observation is a, then find the new mean if each observation is increased by 5 and thendecreased by7

Q.

The number of minutes customers wait at the payment counters at two supermarkets is recorded as under:

Mega Super Market:	3	2	4	6	7	5	4	5	8	4	7	5
Deluxe Super Market	2	6	3	5	4	8	7	8	6	6

Which supermarket had the least mean waiting time ?