A class has an average score of 65. If a new student with a score of 85 joins, h

A class has an average score of 65. If a new student with a score of 85 joins, how does the average change if the class size increases by one?

A class has an average score of 65. If a new student with a score of 85 joins, how does the average change if the class size increases by one?

Step 1: Understand that the average score of the class is 65. This means if there are 'n' students, the total score of all students is 65 times 'n'.
Step 2: Calculate the total score of the class before the new student joins. This is done by multiplying the average score (65) by the number of students (n). So, total score = 65 * n.
Step 3: A new student joins the class with a score of 85. Now, we need to add this score to the total score we calculated in Step 2.
Step 4: The new total score becomes 65 * n + 85.
Step 5: The class size increases by one because of the new student. So, the new number of students is n + 1.
Step 6: To find the new average score, we divide the new total score (65 * n + 85) by the new number of students (n + 1).
Step 7: The formula for the new average is (65 * n + 85) / (n + 1).

Average Calculation – Understanding how to calculate the average score when a new value is added to a set.
Impact of New Data – Analyzing how the addition of a new score affects the overall average of a group.
Algebraic Manipulation – Using algebra to express the new average in terms of the original average and the new score.