15 students took a science test. the average score was 88.0. later in the day a sixteenth student took the same test and scored a 92. the teacher recalculated the class average using all 16 of the scares. by how much will the class average have increased? show your work.
15 * 88 = 1320
1320 + 92 = 1412
1412 / 16 = ?
88.25
To find out how much the class average will have increased, we need to calculate the difference between the initial average score of the 15 students and the new average score including the 16th student.
Here's the step-by-step process:
Step 1: Calculate the initial total score of the 15 students.
Given that the average score of the 15 students is 88, we can multiply it by the total number of students (15) to find the initial total score.
Initial total score = Average score * Number of students
Initial total score = 88 * 15 = 1320
Step 2: Calculate the new total score including the 16th student.
Now that we have the initial total score (1320), we need to add the score of the 16th student (92) to get the new total score.
New total score = Initial total score + Score of the 16th student
New total score = 1320 + 92 = 1412
Step 3: Calculate the new class average.
To find the new class average, we divide the new total score by the total number of students (16).
New class average = New total score / Total number of students
New class average = 1412 / 16 = 88.25
Step 4: Calculate the increase in the class average.
To determine the increase in the class average, we subtract the initial average score (88) from the new class average (88.25).
Increase in class average = New class average - Initial average score
Increase in class average = 88.25 - 88 = 0.25
Therefore, the class average will have increased by 0.25.