Question

Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will

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Timmothy

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To find the new average grade with 26 students, we can follow these steps:

Step 1: Calculate the sum of the original test grades

The sum of the original 25 students' grades is obtained by multiplying the average grade (75) by the number of students (25):

Sum of original grades = 75 * 25 = 1875

Step 2: Add the new student's score to the sum

Now we need to add the new student's score (70) to the sum of the original grades:

Total sum = 1875 + 70 = 1945

Step 3: Calculate the new average grade

To find the new average grade, we divide the total sum by the number of students (26):

New average grade = Total sum / Number of students = 1945 / 26 = 74.81 (rounded to two decimal places)

Answer: The test average grade calculated with 26 students will be approximately 74.81.

Step 1: Calculate the sum of the original test grades

The sum of the original 25 students' grades is obtained by multiplying the average grade (75) by the number of students (25):

Sum of original grades = 75 * 25 = 1875

Step 2: Add the new student's score to the sum

Now we need to add the new student's score (70) to the sum of the original grades:

Total sum = 1875 + 70 = 1945

Step 3: Calculate the new average grade

To find the new average grade, we divide the total sum by the number of students (26):

New average grade = Total sum / Number of students = 1945 / 26 = 74.81 (rounded to two decimal places)

Answer: The test average grade calculated with 26 students will be approximately 74.81.

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