Finding Mean for Grouped Data When Class Intervals Are Not Given

Q. The mean of 40 numbers was found to be 38. Later on, it was detected that a number 56 was misread as 36 . Find the correct mean of the ( data ) given no's

Q.

The arithmetic mean of $1,2,3...n$ is

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

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

3. $\frac{n}{2}$

4. $n$

Q. 1) FIND THE MEAN OF FIRST TEN PRIME NUMBER

Q. Mean is defined as the ratio of the sum of all observations to the total number of observations.

1. False
2. True

Q.

If the arithmetic mean of $a\&b$is $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$, then the value of $n$ is:

1. $-1$

2. $0$

3. $1$

4. None of these

Q. Find the mean of the first ten prime numbers.

Q.

The mean of five number is 30. If one number is excluded their mean become 28. Find the excluded number.

Q.

The marks obtained by $10$ students in a test are $24,30,26,15,22,20,12,25,21$and $x$ and their mean is $21$. Then the value of $x$is-

1. $23$

2. $18$

3. $17$

4. $15$

Q. If the mean of 2, 4, 6, 8, x, y is 5, then find the value of x + y.

Q. Question 15
Let $\overline{x}$ be the mean of $x_1,x_2,\dots \dots x_n$, and $\overline{y}$ be the mean of $y_1,y_2,\dots \dots y_n$. If $\overline{z}$ represents the mean of $x_1,x_2,\dots \dots x_n,y_1,y_2,\dots \dots y_n$, then $\overline{z}$ is equal to:

A) $\overline{x}+\overline{y}$
B) $\frac{\overline{x}+\overline{y}}{2}$
C) $\frac{\overline{x}+\overline{y}}{n}$
D) $\frac{\overline{x}+\overline{y}}{2n}$

Q. Match the following columns:

Column I	Column II
(a) The mean of first 10 odd number =	(p) 11.2
(b) The mean of first 10 even numbers =	(q) 10
(c) The mean of first 10 prime numbers =	(r) 11
(d) The mean of first 10 composite numbers =	(s) 12.9

(a) .......,
(b) .......,
(c) .......,
(d) .......,

Q. The mean of seven numbers is 63. If the six numbers are 65, 70, 68, 59, 73, 55. Find the seventh number.

Q.

What is the mean/average of factors of 20 ?

Q. The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46, find the 6th number.

Q. The following are the heights in centimetres of the students in class X.
162, 155, 166, 173, 170, 161, 166, 151, 167, 176, 178, 175, 163, 165, 170, 152, 172, 166, 176, 159, 157, 158, 148, 174, 152, 162, 171, 178, 157, 145, 148.
The given data has been grouped into class intervals in the given frequency distribution table.
Fill in the table with the missing frequencies.

$\begin{array}{cc}Classinterval& Frequency\left(f_i\right)\\ 145-150& 3\\ 150-155& 3\\ 155-160& p=----\\ 160-165& q=----\\ 165-170& r=----\\ 170-175& s=----\\ 175-180& 5\end{array}$

1. p = 6, q = 4, r = 5, s = 6
2. p = 6, q = 4, r = 4, s = 6
3. p = 5, q = 4, r = 5, s = 6
4. p = 6, q = 5, r = 5, s = 6

Q.

The distribution of height of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table.
$\begin{array}{ccccccc}Height& 110& 115& x_1& 120& 121& 125\\ Numberofstudents& 6& 8& 14& f_1& 4& 3\end{array}$

1. $x_1=118,f_1=15$

2. $x_1=121,f_1=15$

3. $x_1=118,f_1=8$

4. None of the above

Q. The mean of eleven numbers is 47. If a number is added then the mean is increased by 2. Find the new number.

Q. The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value of discarded number is

(a) 98

(b) 99

(c) 100

(d) 101

Q.

$\sum$fx = 5x + 2, $\sum$f = 12. If the mean of the distribution is 6, what is the value of x?

1. 15

2. 18

3. 12

4. 14

Q.

$$\begin{array}{ccc}{x}_i& f_i& f_i{x}_i\\ 4& 10& ........\\ 8& 11& ........\\ 12& 9& .........\\ 16& 13& .........\\ & & \sum f_i{x}_i=..........\end{array}$$

Find the value of $\sum f_i{x}_i$.

1. 40
2. 88
3. 444
4. 208

Q.

A swimming academy has student members of various ages. Student distribution according to age is given below. What is the total number of student members in the academy? ___

$$\begin{array}{cc}Studentageinterval& Numberofstudent\\ 8-10& 7\\ 10-12& 10\\ 12-14& 9\\ 14-16& 13\\ 16-18& 11\\ 18-20& 2\end{array}$$

Q. Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statements is true?

1. The new mean is 4 more than the original mean.
2. The new mean is 4 less than the original mean
3. The new mean is 2 more than the original mean
4. The new mean is equal to the original mean.

Q.

The following are the marks obtained in Maths by students of Class 8:
51, 94, 34, 20, 50, 81, 81, 90, 76, 34, 51, 86, 93, 99, 26, 54, 85, 71, 88, 40, 44, 56, 55, 57, 78, 53, 81, 78, 65, 78.
The data have to be grouped to find the mean marks. One of the class intervals made is 60-70.

What is the frequency of the last class interval?

1. 4
2. 2
3. 8
4. 5

Q.

The mean of the following data $1^2,2^2,3^2,4^2,........n^2$ is ______.

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

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

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

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

Q.

The arithmetic mean of 1, 2, 3, 4, 5, ……., n is ____.

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

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

3. $\frac{n}{2}$

4. $\frac{n}{2}+1$

Q.

The Mean of first 10 natural number is:

1. 5.5

2. 6.5

3. 4.5

4. 5

Q. The mean of 40 numbers was found to be 38. Later on, it was detected that the number 56 was misread as 36. Find the correct mean of the given numbers.

Q.

The mean of the following distribution is ____.
$$\begin{array}{ccccc}{x}_i& \text{10}& \text{13}& \text{16}& \text{19}\\ f_i& \text{2}& \text{5}& \text{7}& \text{6}\end{array}$$

1. 16

2. 15.2

3. 15.35

4. 15.55