A50
B65
C68
D98
Answer:
C. 68
Read Explanation:
Understanding Average (Mean)
The average, also known as the arithmetic mean, is a fundamental statistical measure.
It is calculated by dividing the sum of all values in a dataset by the total number of values.
Formula: Average = (Sum of observations) / (Number of observations).
Concept of Replacement in Averages
When an element (like a person's weight) within a group is replaced by another, the overall sum of the group changes.
This change in sum directly affects the group's average.
If the new element's value is higher than the replaced one, the average will increase.
Conversely, if the new element's value is lower than the replaced one, the average will decrease.
Efficient Approach for Replacement Problems
For competitive exams, these problems can be solved quickly without calculating initial sums.
The total change in sum (or total weight in this case) is directly proportional to the number of items and the change in average.
It is calculated as: Total Change = Number of Items × Change in Average.
The weight of the new person can be found by: New Person's Weight = Replaced Person's Weight + Total Change (if average increases).
If the average decreases, the formula would be: New Person's Weight = Replaced Person's Weight - Total Change.
Step-by-Step Calculation for the Problem
Number of students: 10
Increase in average weight: 2 kg
Weight of the replaced boy: 48 kg
First, calculate the total increase in the collective weight of the 10 students:
Total increase = Number of students × Increase in average
Total increase = 10 × 2 kg = 20 kg
This 20 kg is the extra weight the new boy brings compared to the boy he replaced.
Therefore, the weight of the new boy is:
Weight of new boy = Weight of replaced boy + Total increase
Weight of new boy = 48 kg + 20 kg = 68 kg