Assertion (A) : The mean of 15 observations was found to be 21. Later it was detected that one value 15 was wrongly copied as 18, while calculating the mean. The correct mean is 20.

Reason (R) : The mean of n observations x₁, x₂, x₃, ….., x_n is $\bar{x}$. If each observation is increased by p, then the new mean is increased by p, i.e., the new mean is $\bar{x}$ + p.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Which of the following statements is/are correct?

(i) Mean of a data can be smaller than the smallest number of the data.

(ii) Mean of a data can be bigger than the largest number of the data.

1. Only (i)

2. Only (ii)

3. Both (i) and (ii)

4. Both are wrong

A government agency collected the data of individual incomes of 10,625 people and decided that the individual that have less income than the median of the data are economically poor. Assuming that all the individuals have different incomes, which of the following is correct?

1. The number of economically poor people is less than the number of rich people.

2. The number of economically poor people is more than the number of rich people.

3. Exactly half of the people are economically poor.

4. We can't say anything about the number of economically poor people.

If the mean of a and $\dfrac{1}{a}$ is x, then the mean of a³ and $\dfrac{1}{a^3}$ is :

1. x(4x² - 3)

2. x(x²- 2)

3. x² + 3

4. x²