The 22 students present for a recent test in Ms. Huang’s class had an average score of 88. When students who were absent took the test, three scored 4 points higher than the average and two scored one point higher than the average. What is the new class average when the new scores are included?
total points scored: 22*88 = 1936
Now we add 5 scores, increasing the total by 3*92 + 2*89 = 454
So, the new average for 27 students is
(1936+454)/(22+5) = 88.52
To find the new class average when the new scores are included, we need to calculate the sum of all the scores, including the new scores, and divide it by the total number of students.
Let's break down the solution step by step:
Step 1: Calculate the sum of the original scores.
The original class average of 88 is obtained by multiplying the average score by the number of students. Therefore, the sum of the original scores is 22 students multiplied by the average score of 88: 22 * 88 = 1936.
Step 2: Calculate the sum of the new scores.
We are given that three students scored 4 points higher than the average, so each of these students scored 88 + 4 = 92. Since there were three of them, the sum of their scores is 3 students multiplied by 92: 3 * 92 = 276.
Two other students scored 1 point higher than the average, so each of them scored 88 + 1 = 89. Since there were two of them, the sum of their scores is 2 students multiplied by 89: 2 * 89 = 178.
Therefore, the sum of the new scores is 276 + 178 = 454.
Step 3: Calculate the total number of students.
We already know that there were originally 22 students present for the test. With the students who were absent, the total number of students becomes 22 + 3 + 2 = 27.
Step 4: Calculate the new class average.
To find the new class average, we divide the sum of all the scores, including the new scores, by the total number of students: (1936 + 454) ÷ 27 = 2390 ÷ 27 = 88.52 (rounded to two decimal places).
Therefore, the new class average, when the new scores are included, is approximately 88.52.