Calculating Average Weight of New Students

The question asks us to find the average weight of 6 new students who joined a class, given the initial average weight of the class and how the average weight changed after the new students joined.

Step 1: Calculate the Initial Total Weight

We know the initial number of students and their average weight. The total weight is the number of students multiplied by their average weight.

• Initial number of students = 20
• Initial average weight = 30.5 kg

Initial Total Weight = Initial number of students $\times$ Initial average weight

Initial Total Weight $= 20 \times 30.5$ kg

Initial Total Weight $= 610$ kg

Step 2: Determine the New Number of Students and New Average Weight

6 new students joined the class. The average weight increased by 2 kg.

• Number of new students = 6
• New total number of students = Initial number of students + Number of new students
• New total number of students = $20 + 6 = 26$
• Increase in average weight = 2 kg
• New average weight = Initial average weight + Increase in average weight
• New average weight = $30.5$ kg + $2$ kg = $32.5$ kg

Step 3: Calculate the New Total Weight

Now that we know the new total number of students and the new average weight, we can find the new total weight of the class.

New Total Weight = New total number of students $\times$ New average weight

New Total Weight $= 26 \times 32.5$ kg

New Total Weight $= 845$ kg

Step 4: Calculate the Total Weight of the New Students

The difference between the new total weight and the initial total weight is the total weight of the 6 new students who joined.

Total weight of 6 new students = New Total Weight - Initial Total Weight

Total weight of 6 new students $= 845$ kg - $610$ kg

Total weight of 6 new students $= 235$ kg

Step 5: Calculate the Average Weight of the New Students

To find the average weight of the 6 new students, divide their total weight by the number of new students.

Average weight of 6 new students = Total weight of 6 new students / Number of new students

Average weight of 6 new students $= \frac{235}{6}$ kg

Calculating the value:

$\frac{235}{6} \approx 39.1666...$ kg

Step 6: Round the Average Weight to One Decimal Place

The question asks for the answer rounded off to one decimal place.

$39.1666...$ kg rounded to one decimal place is $39.2$ kg.

Therefore, the average weight of the 6 new students who joined the class is approximately 39.2 kg.

Revision Table: Key Data Points

Additional Information: Understanding Average

The average (or mean) of a set of numbers is calculated by summing all the numbers in the set and then dividing by the count of numbers in the set. In this problem, the average weight is the total weight of all students divided by the number of students.

Formula for Average = $\frac{\text{Sum of all values}}{\text{Number of values}}$

When new items (in this case, students with their weights) are added to a group, the total sum changes, and the number of items changes. The new average reflects these changes.

If the new average is higher than the old average, it means the new items added (the new students) must have had a total value (total weight) greater than the old average weight, and specifically, great enough to pull the overall average up.