Average marks obtained by students of a class in an exam is 70. Which of the following is definitely incorrect?

(i) One of the students scored more than 100 marks.

(ii) One of the students scored less than 10 marks.

1. Only (i)

2. Only (ii)

3. Both (i) and (ii)

4. None of these

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.

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5. The mean of the given numbers is :

1. 49.5

2. 53

3. 46.5

4. 56.5

There are 10 observations x₁, x₂, x₃, ….., x₁₀ in a data. The first five elements x₁, x₂, ….., x₅ are placed by x₁ + 5, x₂ + 5, ….., x₅ + 5 respectively. Also, the next five elements x₆, x₇, ….., x₁₀ are placed by x₆ - 5, x₇ - 5, …, x₁₀ - 5 respectively. Calculate the overall change in the mean of the data.