Calculating Student Weight Using Average Concepts

This problem involves understanding the concept of average and how it changes when an element (in this case, a student's weight) is removed from a set. The average weight of a group is calculated by dividing the total weight of all individuals by the number of individuals in the group.

Initial Average Weight Calculation

Initially, we have 15 students in the class, and their average weight is given as 40 kg. The formula for average is:

$$ \text{Average Weight} = \frac{\text{Total Weight}}{\text{Number of Students}} $$

We can rearrange this formula to find the total weight:

$$ \text{Total Weight} = \text{Average Weight} \times \text{Number of Students} $$

Using the initial values:

• Number of Students initially = 15
• Average Weight initially = 40 kg

So, the initial total weight of the 15 students is:

$$ \text{Initial Total Weight} = 40 \text{ kg/student} \times 15 \text{ students} $$

$$ \text{Initial Total Weight} = 600 \text{ kg} $$

Average Weight After One Student Leaves

When one student leaves the class, the number of students decreases, and the average weight changes to 39.5 kg.

• Number of Students after one leaves = 15 - 1 = 14
• Average Weight after one leaves = 39.5 kg

Now, we calculate the total weight of the remaining 14 students:

$$ \text{New Total Weight} = \text{New Average Weight} \times \text{New Number of Students} $$

$$ \text{New Total Weight} = 39.5 \text{ kg/student} \times 14 \text{ students} $$

Let's calculate $39.5 \times 14$:

$$ 39.5 \times 14 = (40 - 0.5) \times 14 $$

$$ = 40 \times 14 - 0.5 \times 14 $$

$$ = 560 - 7 $$

$$ = 553 \text{ kg} $$

So, the total weight of the remaining 14 students is 553 kg.

Finding the Weight of the Student Who Left

The difference between the initial total weight and the new total weight is exactly the weight of the student who left the class. This is because the total weight reduced only due to the removal of that one student.

$$ \text{Weight of Student Who Left} = \text{Initial Total Weight} - \text{New Total Weight} $$

$$ \text{Weight of Student Who Left} = 600 \text{ kg} - 553 \text{ kg} $$

$$ \text{Weight of Student Who Left} = 47 \text{ kg} $$

Therefore, the weight of the student who left the class is 47 kg.

Comparing with Options

Let's look at the given options:

• 47 kg
• 42 kg
• 52 kg
• 48 kg

Our calculated weight of the student who left is 47 kg, which matches the first option.

Revision Table: Average Weight Problem

Additional Information: Concepts Related to Average and Sum

The average is a fundamental concept in statistics, representing the central value of a set of numbers. It's often called the mean.

• Sum: The total value obtained by adding up all the numbers in a set. In this problem, the 'total weight' is the sum of the weights of all students.
• Count: The number of items or values in the set. Here, the 'number of students' is the count.
• Relationship: Average, Sum, and Count are related by the formula: $\text{Average} = \frac{\text{Sum}}{\text{Count}}$. Knowing any two allows you to find the third.
• Changes in Average: When an item is added or removed from a set, the sum changes, and often the count changes as well (unless replacing an item). This causes the average to change. We can use the change in total sum to find the value of the item added or removed.

Understanding how these concepts interact is crucial for solving problems involving averages of changing groups.