Period 1 has 15 students in it and a test average of 86%. Period 2 has 21 students in it and an average of 88%. Period 3 has 12 students in it and an average of 95%. Use weighted means to find the overall average of the classes.
total marks of students in period 1 = 86*15 = 1290
total marks of students in period 2 = 88*21 = 1748
total marks of students in period 3 = 95*12 = 1140
add them up, then divide by the total number of students.
87.3
To find the overall average of the classes using weighted means, we need to consider both the number of students in each class and their respective averages.
Step 1: Multiply the number of students in each class by their average.
For Period 1: 15 * 86% = 1290
For Period 2: 21 * 88% = 1848
For Period 3: 12 * 95% = 1140
Step 2: Add up the results from Step 1.
1290 + 1848 + 1140 = 4278
Step 3: Calculate the total number of students.
15 + 21 + 12 = 48
Step 4: Divide the sum from Step 2 by the total number of students from Step 3.
4278 / 48 = 89.125
Therefore, the overall average of the classes using weighted means is approximately 89.125%.
To find the overall average of the classes using weighted means, we need to multiply the average of each period by the number of students in that period, and then add up these values. Finally, divide the sum by the total number of students.
Let's calculate this step by step:
Step 1: Find the weighted sum for each period
For Period 1: Weighted sum = 15 (number of students) * 86% (average) = 1,290
For Period 2: Weighted sum = 21 * 88% = 1,848
For Period 3: Weighted sum = 12 * 95% = 1,140
Step 2: Find the total number of students
Total number of students = 15 + 21 + 12 = 48
Step 3: Find the overall weighted average
Overall weighted average = (Weighted sum for Period 1 + Weighted sum for Period 2 + Weighted sum for Period 3) / Total number of students
= (1,290 + 1,848 + 1,140) / 48
= 4,278 / 48
≈ 89.13%
Therefore, the overall average of the classes, using weighted means, is approximately 89.13%.