Mathematical Expression for Mean

Q.

If the arithmetic mean and geometric mean of the $pth$ and $qth$ terms of the sequence $-16,8,-4,2,\dots .$ satisfy the equation $4x^2-9x+5=0$, then $p+q$ is equal to

Q.

Find The Average Of First Ten Prime Numbers?

Q.

The enrolment in a school during six consecutive years was as follows: $1555,1670,1750,2013,2540,2820.$ Find the mean enrolment of the school for this period.

Q.

What is the difference between harmonic mean and arithmetic mean?

Q. The mean weight of a group of seven boys is 56 kgs. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy. [4 MARKS]

Q. Question 3
Calculate the mean of the following data
$\begin{array}{ccccc}\text{Class}& 4-7& 8-11& 12-15& 16-19\\ \text{Frequency}& 5& 4& 9& 10\end{array}$

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

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

Q.

Formulas of statistics

Q. The mean of n items is $\overline{x}$. If the first item is increased by 1, second by 2 and so on, then the new mean is ____.

1. $\overline{X}+n$
2. $\overline{X}+\frac{n}{2}$
3. $\overline{X}+\frac{n+1}{2}$
4. None of the above

Q.

If $x_i>0,i=1,2,3,...n$ then $\left(x_1+x_2+...+x_n\right)\left(\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}\right)$ is equal to

1. $n^2$

2. $\ge n^2$

3. $\le n^2$

4. None of these

Q.

The mean of the series $a,a+nd,a+2nd$ is

1. $a+(n-1)d$

2. $a+nd$

3. $a+(n+1)d$

4. None of these

Q.

The value of $n$ for which $\frac{x^{n+1}+y^{n+1}}{x^n+y^n}$ is the geometric mean of $x$ and $y$ is

1. $-\frac{1}{2}$

2. $\frac{1}{2}$

3. $1$

4. $-1$

Q.

How do I prove the relation between $AM,GM$ and $HM?$

Q.

Cathy has obtained a sample mean of $0.7$ and $\sum _{\text{i}=1}^{\text{n}}{x_{\text{i}}}^2=10$ , but she cannot remember if the sample size was $20$ or $25$. She accidentally erased the data file. Find the correct sample size.

Q. The means of a set of numbers is $\overline{X}$. If each number is divided by $3$, then the new mean is

1. $\overline{X}$
2. $\overline{X}+3$
3. $3\overline{X}$
4. $\frac{\overline{X}}{3}$

Q.

The mean of the following distribution is:

$$\begin{array}{ccccc}{x}_i& 15& 12& 18& 19\\ f_i& 2& 5& 7& 6\end{array}$$

1. 15.55

2. 16

3. 15.2

4. 15.35

Q. If the mean of first $n$ natural numbers is $\frac{5n}{9}$, then $n=$

1. $9$
2. $5$
3. $4$
4. none of these

Q. The mean of $10$ numbers is $7$ If each number is multiplied by $12$ then the mean of new set of numbers is

1. $78$
2. $84$
3. $82$
4. $48$

Q. The mean weight of $120$ students in the second year class of a college is $56kg$, If the mean weight of the boys and that of the girls in the class are $60kg$ and $50kg$ respectively, then the number of boys and girls separately in the class are

1. $38,64$
2. $72,48$
3. None of these
4. $72,64$

Q.

If $N$arithmetic means are inserted between $1$and $31$ such that ratio of first and $n^{th}$mean is $3:29,$then what is the value of $N$?

Q. Use log table to find log 86.76

1. 0.9383
2. 1.9383
3. 0.0003
4. 0.8633

Q.

The following table shows the marks obtained by 5 students in a class. What is the average marks of the class?

$$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 98& 1\\ 65& 1\\ 88& 2\\ 54& 1\end{array}$$

1. 76.6

2. 77.6

3. 78.6

4. 78.9

Q. If each of $n$ numbers $x_i=i$ is replaced by $(i+1)x_i$, then the new mean is

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

Q.

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:

3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6.

Now, the mean of the weights of the babies will be

1. 4

2. 9

3. 7.2

4. 6

Q. If $\overline{x}$ is the mean of the terms $x_1,x_2,x_3,...x_n$ and
$\sum _{i=1}^n{x}_1=x_1,x_2,x_3+......x_n$, then the value of $\sum _{i=1}^n{x}_i-n\overline{x}$

1. $1$
2. $n$
3. $x$
4. $0$

Q. In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each. Remaining students brought at least one book each and no two students brought the same number of books. If the average number of books brought in the class is a positive integer then what could be the total number of books brought by the remaining students?

1. 12
2. 16
3. 14
4. 8

Q. The marks obtained by 12 students in an examination (out of $50$) are given below.
$18,35,2,27,40,0,21,33,27,8,36,23$
Find the mean marks.

Q. Which type of average is most affected by extreme values in the data?

1. Mean
2. Mode
3. Median
4. All of the above

Q. multiplied by $2$

1. $60$
2. $55$
3. $64$
4. $50$

Q. increased by $3$

1. $30$
2. $32$
3. $34$
4. $35$