The runs scored by a cricketer in last 20 innings are given below.

The mean runs of the cricketer per inning is :

1. 21

2. 24

3. 29

4. 30

Case Study:
A school organized a Health Check Up Camp for its students. The weights (in kg) of the students of a class were recorded as below :

41, 40, 36, 52, 50, 48, 47, 45,
40, 41, 42, 49, 50, 51, 38, 41,
40, 45, 40, 39, 49, 51, 48, 46,
44, 50, 57, 38, 41, 51

Based on the above information, answer the following questions:

1. The range of the data is :
   (a) 20 kg
   (b) 21 kg
   (c) 22 kg
   (d) 23 kg

2. Mean weight of the data is :
   (a) 45 kg
   (b) 44.5 kg
   (c) 42.5 kg
   (d) 40.5 kg

3. Median of the data is :
   (a) 44 kg
   (b) 45 kg
   (c) 45.5 kg
   (d) 46 kg

4. One student weighing 45 kg, was absent on that day. Next day, the teacher added his name in the list. The average weight of the new group is :
   (a) 47 kg
   (b) 46.4 kg
   (c) 46 kg
   (d) 45 kg

5. The median weight of the students after adding the absentee in the list is :
   (a) 45 kg
   (b) 46 kg
   (c) 44.5 kg
   (d) 44.2 kg

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