Mean

Q.

A lift can carry up to $8$ persons. At the ground floor$A,B,C$ whose weights are in increasing AP with an average weight of $62kg$ enter the lift. When the lift stops at $3rd$ floor $E,FandG$ whose weights are in an increasing AP enter the lift. The new average weight of people in the lift becomes $66kg$. What is the weight of F?

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. $60\%$
2. $50\%$
3. $30\%$
4. $40\%$

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 if $55$kg, then number of boys and girls respectively are

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

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 difference between mean and mode is $63$, then the difference between mean and median is

1. $189$
2. $21$
3. $31$
4. $48$

Q.

Calculate the mean, median and standard deviation of the following distribution :

$\begin{array}{ccccccccc}textClass-interval:& 31-35& 36-40& 41-45& 46-50& 51-55& 56-60& 61-65& 66-70\\ \text{Frequency}:& 2& 3& 8& 12& 16& 5& 2& 3\end{array}$

Q. The mean of $10$ numbers $7\times 8,10\times 10,13\times 12,16\times 14,....$ is

Q.

The mean age of 50 persons was found to be 32 years. Later it was detected that the age 28 was wrongly noted as 35, the age 57 was wrongly noted as 30 and the age 60 was wrongly noted as 32. Then the correct mean age is

1. 28

2. 33

3. 31

4. 32.4

Q. If $X$ is a random variable such that $\sigma \left(X\right)=2.6$, then $\sigma (1-4X)$ is equal to,

1. $-10.4$
2. $10.4$
3. $7.8$
4. $13$

Q.

Let in a series of $2\mathrm{n}$ observations, half of them are equal to$\mathrm{a}$ and the remaining half are equal to $-\mathrm{a}$. Also by adding a constant$\mathrm{b}$ in each of these observations, the mean and standard deviation of the new set become$5$ and $20$, respectively. Then the value of ${\mathrm{a}}^2+{\mathrm{b}}^2$ is equal to:

1. $250$

2. $925$

3. $650$

4. 425

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 added to the data, then the mean of the resultant data is

1. 14.0

2. 16.8

3. 16.0

4. 15.8

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

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

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

1. $68$
2. $70$
3. $71$
4. $65$

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

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

1. 
2. 
3. 
4. 

Q. The mean and the standard deviation(s.d.) of five observations are $9$ and $0$, respectively. If one of the observation is changed such that the mean of the new set of five observations becomes $10$, then their s.d. is :

1. $0$
2. $1$
3. $4$
4. $2$

Q. If the arithmetic mean of the number $x_1,x_2,x_3.........,x_n$ is $\overline{x}$ , then the arithmetic mean of numbers$a{x}_1,+b,a{x}_2+b,a{x}_3+b,.............a{x}_n+b,$
where a, b are two constants would be

1. $\overline{x}$
2. $na\overline{x}+nb$
3. $a\overline{x}$
4. $a\overline{x}+b$

Q. Mean of $100$ observations is $45$. It was later found that two observations, $19$ and $31$ were incorrectly recorded as $91$ and $13$ respectively. Then the correct mean is

1. $44.2$
2. $44.4$
3. $44.42$
4. $44.46$

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 frequency distribution of discrete data is given below, the frequency $x$ against value $0$ is missing
If the mean is $2.5$, then the missing frequency $x$ will be

$\begin{array}{ccccccc}\text{Variable}& 0& 1& 2& 3& 4& 5\\ \text{Frequency}& x& 20& 40& 40& 20& 4\end{array}$

1. $0$
2. $1$
3. $3$
4. $4$

Q.

Find the harmonic mean of 1, $\frac{1}{2}$, $\frac{1}{3}$.

1. 2

2. 

3. 3

4. 

Q. A boat, while going downstream in a river covered a distance of $50$ miles at an average speed of $60$ mph. While returning, because of the water resistance, it took $1$ hour $15$ minutes to cover the same distance. What was the average speed during the whole journey?

1. $40$ mph
2. $48$ mph
3. $50$ mph
4. $55$ mph

Q.

If the mean and variance of eight numbers $3,7,9,12,13,20,x$ and $y$ be $10$ and $25$ respectively then $xy$ is equal to

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. A 100 mark examination was administered to a class of 50 students. Despite only integer marks being given, the average score of the class was 47.5. Then, the maximum number of students who would get marks more than the class average are

1. 25
2. 35
3. 49
4. 45

Q.

The mean number of tails in three tosses of a fair coin is:

1. 3

2. 6

3. 3/2

4. 1/6

Q.

The following table shows the weight (in kg.) of $50$ persons:

Weight (in kg)	$42$	$47$	$52$	$57$	$62$	$67$	$72$
Number of persons	$3$	$8$	$6$	$8$	$11$	$5$	$9$

Find the mean, median and mode.

Q. A factory is operating in two shifts, day and night, with $70$ and $30$ workers respectively. If per day mean wage of the day shift workers is Rs. $54$ and per day mean wage of all the worker is Rs. $60$, then per day mean wage of the night shift workers (in Rs.) is

1. $75$
2. $69$
3. $66$
4. $74$