Mean

Q. Find the mean of the following data by shortcut method.

Marks	20	22	25	30	35	39	45	50	Total
Frequency	4	6	8	10	8	7	5	2	50

Q.

The mean of marks scored by $100$ students was found to be $40.$ Later on it was discovered that a score of $53$ was misread as $83.$ Find the correct mean.

Q.

Question 6
The table below shows the daily expenditure on food of 25 households in a locality.

$\begin{array}{cccccc}\text{Daily expenditure (in Rs)}& 100-150& 150-200& 200-250& 250-300& 300-350\\ \text{Number of households}& 4& 5& 12& 2& 2\end{array}$

Find the mean daily expenditure on food by a suitable method.

Q. The mean of 16 numbers is 8.if 2 is added to every number , what is the new mean?

Q.

What is the arithmetic mean of first $n$ natural numbers?

Q.

The arithmetic mean of first $n$ odd natural numbers is:

1. $n^2$

2. $2n$

3. $n$

4. $3n$

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. Question 12
If the mean of the observations x, x+3, x+5, x+7 and x+10 is 9, then mean of the last three observation is:

A) $10\frac{1}{3}$
B) $10\frac{2}{3}$
C) $11\frac{1}{3}$
D) ​​​​​​​$11\frac{2}{3}$​​​​​​​

Q.

If the mean of $x$ and $\frac{1}{x}$ is $M$, then the mean of $x^2$ and $\frac{1}{x^2}$ is

1. $2M^2-1$
2. $2M^2+1$
3. $2M^2\times 1$
4. $2M^2-2$

Q.

The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean rises by 500 g.
Find the weight of the teacher.

Q.

If the mean of five observations $x,x+2,x+4,x+6,x+8$ is $11$, then the mean of first three observations is:

1. $9$

2. $8$

3. $7$

4. $6$

Q. Find the class-mark of the class 35-40.

Q. Mean of 100 observations is found to be 40. At the time of computation two items were wrongly taken as 30 and 27 instead of 3 and 72. Find the correct mean.

Q.

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. The correct mean is
(a) 38.6
(b) 39.4
(c) 39.8
(d) 39.2

Q.

The average weight of a class of 39 students is 40 kg. When a new student is admitted to the class, the average decreases by 200 g. Find the weight of the new student.

Q.

Question 12
Mean of 50 observations was found to be 80.4. But later on, it was discovered that 96 was misread as 69 at one place. Find the correct mean.

Q.

The mean of 100 observations is 50. If one of the observations 50 is replaced by 150, the resulting mean will be
(a) 50.5
(b) 51
(c) 51.5
(d) 52

Q.

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

Q.

The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 k& 46 kg and 44 kg.
Find the weight of the sixth boy.

Q.

Find the mean of the factors of 12.

1. $16$

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

3. $\frac{14}{3}$

4. $3$

Q.

If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value of x is

1. 10

2. 12

3. 14

4. 16

Q. The mean of 100 items was found to be 30. If at the time of calculation, two items were wrongly taken as 32 and 12 instead of 23 and 11, then the correct mean is -

1. 
   29.8
2. 
   28.8
3. 
   29.9
4. 
   28.9

Q.

The mean of 10 numbers is 55. If one number is excluded, their mean becomes 50, the excluded number is:

1. 80

2. 100

3. 70

4. 60

Q. The mean of 10 observations is 42 If each observation in data is decreased by 12 What will be the new mean of data

Q.

The average weekly payment to $75$ workers in a factory is $Rs.5680$. The mean weekly payment to $25$ of them is $Rs.5400$ and that of $30$ others is $Rs.5700$. Find the mean weekly payment of the remaining workers.

Q.

The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man. Find the weight of the new man.

Q.

Question 11
A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 ( out of 100) and that of boys is 71. Determine the mean score of the whole class.

Q. The mean of n observations is X. If k is added to each observation, then the new mean is

(a) X

(b) X + k

(c) X − k

(d) kX

Q. The mean of 8 observations is 40. If 5 is added to each observation, then find the value of the new mean.

Q.

Mean of 20 observations is 15.5. Later it was found that the observation 24 was misread as 42. The corrected mean is:

1. 14.6

2. 14.2

3. 14.8

4. 14.0