The mean weight of 40 students is 50 kg. One of the student leave and is replaced by another student which reduces the mean weight of the class by 0.5 kg. If the weight of the student who left is 65kg, what is the weight of the student who joined the class.
Mean = Σx/n
50 = Σx/40
Σx = 2000
49.5 = (2000-65+x)/40
Solve for x.
To find the weight of the student who joined the class, we need to understand how mean (average) weight is calculated and how it changes when a student leaves and another student joins.
Let's start by calculating the initial total weight of the 40 students before any changes were made. We know that the mean weight of the 40 students is 50 kg.
Mean weight = Total weight / Number of students
Substituting the known values:
50 kg = Total weight / 40 students
To find the total weight, we can rearrange the equation:
Total weight = Mean weight * Number of students
Total weight = 50 kg * 40 students
Total weight = 2000 kg
Now, let's consider the change that occurs when a student leaves the class. We know that the weight of the student who left is 65 kg. To account for this change, we need to subtract the weight of the student who left from the total weight.
New total weight = Total weight - Weight of student who left
New total weight = 2000 kg - 65 kg
New total weight = 1935 kg
Next, let's consider the change that occurs when a new student joins the class and reduces the mean weight by 0.5 kg. To calculate the weight of the student who joined, we need to find the new mean weight using the new total weight and the number of students.
Mean weight = New total weight / Number of students
Substituting the known values:
Mean weight - 0.5 kg = 1935 kg / 40 students
To find the new total weight, we can rearrange the equation:
New total weight = (Mean weight - 0.5 kg) * Number of students
New total weight = (1935 kg) * 40 students
Now we have two equations related to the total weight:
New total weight = (Mean weight - 0.5 kg) * Number of students
New total weight = (1935 kg) * 40 students
By setting these two equations equal to each other, we can solve for the mean weight:
(Mean weight - 0.5 kg) * Number of students = (1935 kg) * 40 students
Simplify the equation:
Mean weight - 0.5 kg = 1935 kg
Now solve for the mean weight:
Mean weight = 1935 kg + 0.5 kg
Mean weight = 1935.5 kg
Finally, to find the weight of the student who joined the class, we can subtract the total weight of the other 39 students from the mean weight:
Weight of the student who joined = Mean weight - Total weight of other 39 students
Weight of the student who joined = 1935.5 kg - 1935 kg
Weight of the student who joined = 0.5 kg
Therefore, the weight of the student who joined the class is 0.5 kg.