Arithmetic Mean by Deviation Method

Q. The sum of deviations of 'n' observations from 20 is 20 and sum of deviations same 'n' observations from 30 is - 20 . Find the mean of the observations.

1. 50
2. 35
3. 25
4. 20

Q.

In the formula $\overline{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$ , the "a" stands for assumed mean.

1. False

2. True

Q. Find the sum of deviations of all the observations of the data 4 , 10 , 23 , 12 , 14 , 21 from their mean.

1. 0
2. 14
3. 1
4. -4

Q. The arithmetic mean of marks scored by 10 students was 20. Nikhil, one of the students, inquired other 9 students and recorded their deviation from his marks as -5, 6, 2, -2, 0, 2, 4, -3, 6. Find the marks of Nikhil.

1. 15
2. 17
3. 19
4. 21

Q. Define standard deviation.

Q. Estimated mean becomes the actual arithmetic mean if _______.

1. Deviations are greater than median
2. Mode is greater than median
3. Sum of deviations exceeds the number of observations
4. Average of deviations is zero.

Q. Sum of deviations of all the observations of the data 14, 7, 32, 15, 18, 23, 38 from their mean is .

1. 1
2. \N
3. 12
4. -4

Q. Find the arithmetic mean of the five observations 14, 56, 23, 44, 23 where the estimated mean is given as 30.

1. 30
2. 32
3. 33
4. 31

Q. Share price of a MRF stock through a week is varying as ₹34232 , ₹44532 , ₹23442 , ₹54433 , ₹42221 , ₹53222 and ₹34632. Find the average share price of the stock by deviation method.

1. 41187.71
2. 411871.1
3. 41287.71
4. 41387.71

Q. In the assumed mean method, if A is the assumed mean, then deviation $d_i$ is _____.

1. $x_i-A$
2. $A-x_i$
3. $x_i$
4. $-(A-x_i)$

Q. Score and estimated mean are given in the table below. Find the value of arithmetic mean.

Score	Estimated Mean
7	17
10	17
15	17
21	17
27	17

1. 15
2. 16
3. 17
4. 18

Q. The algebric sum of deviations of $10$ observations measured from $15$ is $7$. The mean is

1. $70$
2. $105$
3. $15.7$
4. none of these

Q.

Σfx = 6Y - 4, Σf = 8. If the mean of the distribution is 7, what is the value of Y?

1. 9

2. 10

3. 11

4. 12

Q. If the sum of the deviations of all the 35 observations from the average is 150, then find the mean deviation.

1. 4
2. 3.6
3. 3.45
4. 4.29

Q. If the sum of the deviations of all the 40 observations from the average is 160, then find the average of deviations.

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

Q.

The arithmetic mean of the following data is

1. 18.56

2. 20

3. 17.3

4. 19.92

Q.

The algebraic sum of the deviations of a frequency distribution from its mean is :

1. Non – zero number
2. Always positive
3. 0
4. Always negative

Q. $\{9,12,15,18,21\}$
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?
I. $14,16$
II. $9,21$
III. $15,100$

1. II only
2. III only
3. I, II, and III
4. I and II
5. II and III

Q. What is the correct formula for Arithmetic Mean by Deviation Method?

1. Arithmetic mean = Estimated mean + Sum of Deviations
2. Arithmetic mean = Estimated mean - Sum of deviations
3. Arithmetic mean = Estimated mean + Average of deviations
4. Arithmetic mean = Estimated mean - Average of deviations

Q. The difference between any score of data and the assumed mean is called _______.

1. average of deviations
2. deviations
3. regular difference
4. mean