Mean

Q. In the following table, the no. of students and their marks are given

$\begin{array}{ccccccc}\text{No. of students}& 8& 12& 20& 10& 6& 4\\ \text{Marks}& 20& 30& 40& 50& 60& 70\end{array}$
The mean score of students will be

1. $41$
2. $42$
3. $40$
4. $39$

Q. The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is

1. 30
2. 40
3. 50
4. 60

Q. If the average wages of a worker during a fortnight comprising $15$ consecutive working days was $90\$$ per day.
During the first $7$ days, his average wages was $87\$$ units per day and the average wages during the last $7$ days was $92\$$ per day. Then his wage on the $8^{th}$ day is

1. $97~\$
2. $90~\$
3. $83~\$
4. $92~\$

Q. The reciprocal of the mean of the reciprocals of n observations is their

1. A.M
2. G.M
3. H.M
4. None of these

Q. Median of the odd divisors of $360$ is

1. Mean of $3^{\text{rd}}\text{\&}{4}^{\text{th}}$ observations
2. Mean of $4^{\text{th}}\text{\&}{5}^{\text{th}}$ observations
3. Mean of $5^{\text{th}}\text{\&}{6}^{\text{th}}$ observations
4. Mean of $6^{\text{th}}\text{\&}{7}^{\text{th}}$ observations

Q. A distribution consists of three components with frequencies $300,200$ and $600$ having their means $16,8$ and $4$ respectively, then the mean of combined distribution is

Q. The A.M. of a 50 set of 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. 38.5
2. 37.5
3. 36
4. 36.5

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.

What can be inferred if the Range of one data set is higher than other derived from the same experiment?

1. Values are scattered farther in $1^{st}$ case compared to $2^{nd}$ case

2. Maximum value of $1^{st}$ case > maximum value in $2^{nd}$case

3. Minimum value of $1^{st}$ case > minimum value in $2^{nd}$ case

4. Difference between maximum and minimum in $1^{st}$ case is greater compared to $2^{nd}$ case

Q. The arithmetic mean of $5$ consecutive integers starting with ${}^{\prime }{s}^{\prime }$ is ${}^{\prime }{a}^{\prime }.$ Then the arithmetic mean of $9$ consecutive integers that start with $s+2$ is

1. $2+a+s$
2. $22+a$
3. $2s$
4. $a+4$

Q. The mean weight per student in a group of seven students is 55 kg if the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weight of the seventh student is

1. 57 kg
2. 50 kg
3. 55 kg
4. 60 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. $Thearithmeticmeanoftheseries{}^n{c}_0{,}^n{c}_1{,}^n{c}_2.....{,}^n{c}_{n}is:$

1. $\frac{2^n}{n+1}$
2. $\frac{2^n}{n}$
3. $\frac{2^n-1}{n+1}$
4. none of these

Q. Mean of $n$ items is $\overline{x}$. If these $n$ items are successively increased by $2,2^2,2^3,..,2^n$, then the new mean is

1. $\overline{x}+\frac{2^{n+1}}{n}$
2. $\overline{x}+\frac{2^{n+1}}{n}-\frac{2}{n}$
3. $\overline{x}+\frac{2^n}{n}$
4. $\overline{x}+2^n$

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. $\overline{x}$
2. $\lambda +\overline{x}$
3. $\lambda \overline{x}$
4. None of these

Q. The mean of the values $0,1,2,\dots \dots \dots ,n$ having corresponding weight ${}^n{C}_0{,}^n{C}_1{,}^n{C}_2,\dots \dots \dots {\dots }^n{C}_n,$ respectively is

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

Q. Let the mean of $n$ terms be $\overline{x}$, if the first term is increased by $1$, second term is increased by $2$ and so on, then the new mean is

1. $\overline{x}+n$
2. $\frac{\overline{x}+n}{2}$
3. $\overline{x}+\left(\frac{n+1}{2}\right)$
4. $\overline{x}+\left(\frac{n-1}{3}\right)$

Q.

If the mean of 1, 2, 3, .........., n is $\frac{6n}{11}$, then n is

1. 10

2. 12

3. 11

4. 13

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. 60

3. 40

4. 20

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. The mean of the data set comprising of $16$ observations is $16.$ If one of the observations valued $16,$ is deleted and three new observations valued $3,4$ and $5$ are added to the data set, then the mean of the resultant data is

Q. The A. M. of n observations is M. If the sum of n - 4 observations is a, then the mean of remaining 4 observations is

1. $\frac{nM-a}{4}$
2. $\frac{nM+a}{4}$
3. $\frac{nM-A}{2}$
4. $nM+a$

Q. If ${\overline{x}}_1$ and ${\overline{x}}_2$ are the means of two distributions such that ${\overline{x}}_1<{\overline{x}}_2$ and $\overline{x}$ is the mean of the combined
distribution, then

1. $\overline{x}<{\overline{x}}_1$
2. $\overline{x}>{\overline{x}}_2$
3. $\overline{x}=\frac{{\overline{x}}_1+{\overline{x}}_2}{2}$
4. ${\overline{x}}_1<\overline{x}<{\overline{x}}_2$

Q.

The mean of the series $x_1,x_2,x_3,.......,x_n$ is $\overline{x}$. If $x_2$ is replaced by $\lambda$, then the new mean is

1. $\overline{x}-x_2+\lambda$
   

2. $\frac{\overline{x}-x_2-\lambda }{n}$
   

3. $\frac{(n-1)\overline{x}+\lambda }{n}$
   

4. $\frac{n\overline{x}-x_2+\lambda }{n}$

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

1. $\frac{1}{3}(2n+1)$
2. $\frac{1}{2}(n+4)$
3. $\frac{1}{5}(2n+3)$
4. None of these

Q. The mean of the values $0,1,2,\dots \dots \dots ,n$ having corresponding weight ${}^n{C}_0{,}^n{C}_1{,}^n{C}_2,\dots \dots \dots {\dots }^n{C}_n,$ respectively is

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

Q. Mean of numbers $\frac{{}^{50}{C}_0}{1},\frac{{}^{50}{C}_2}{3},\frac{{}^{50}{C}_4}{5},\cdots ,\frac{{}^{50}{C}_{50}}{51}$ is

1. $\frac{2^{49}}{663}$
2. $\frac{2^{50}}{663}$
3. $\frac{2^{49}}{51}$
4. $\frac{2^{49}}{54}$

Q. A sequence consists of $7$ terms arranged in descending order. Then mean value of the sequence is $70.$ If $30$ is added to each term and then each term is divided by $2$, then

1. the absolute value of difference between new mean and old mean is $15$
2. the absolute value of difference between new mean and old mean is $20$
3. the absolute value of difference between new mean and old mean is $0$
4. the position of new median will not change.

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. If the mean of 3, 4, x, 7, 10 is 6, then the value of x is

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