The average of 4.5, 3.0, 2.7, 1.8 and 4 is
Answers
Answer:
Step-by-step explanation:
Weighted average (weighted arithmetic mean) is a concept similar to standard arithmetic mean (called simply the average), but in the weighted average not all elements are contributing equally to the final result. We can say that some values are more important than the others, so they are multiplied by a coefficient called the weight.
For example, during your studies you may encounter the situation where the grade from an exam is two times more important than the grade from a quiz - and that's exactly what we call the weighted average method. To define it in a more mathematical way, we can write the weighted average formula as:
weighted mean formula
where x1,x2...xn are our numbers, and w1,w2...wn are our weights - the importance of the numbers in averaging.
So, having A from an exam and C from a quiz, you'd get B as a standard average, but assuming that the exam is two times more important, you should get a B+.
How to calculate a weighted average
One type of average which is typically weighted is a grade point average. As the calculation of GPA may sometimes be tricky, we've created two dedicated tools: the high school GPA and the college GPA calculator - have you checked them yet?
Let's find out how to calculate a weighted average - the easiest way is to look at the simple example:
Suppose a student has two four-credit classes, a three-credit class, and a two-credit class. Assume that the grades of the courses are as follows:
A for a four-credit class,
B for the other four credit class,
A for the three credit class,
C+ for the two credit class.
Then, we need to translate the letter grades into numerical values. Most schools in the US use a so-called 4.0 GPA scale, which is a 4 point grading scale. The table below shows a typical letter grade/GPA conversion system:
Letter Grade Percentile 4.0 scale +4.0 scale
A+ 97-100 4 4.3
A 93-96 4 4
A- 90-92 3.7 3.7
B+ 87-89 3.3 3.3
B 83-86 3 3
B- 80-82 2.7 2.7
C+ 77-79 2.3 2.3
C 73-76 2 2
C- 70-72 1.7 1.7
D+ 67-69 1.3 1.3
D 65-66 1 1
F Below 65 0 0
So from the table we know that A = 4.0, B = 3.0 and C+ = 2.3. Now that we have all the information, we can have a look at how to calculate the GPA using a weighted average method:
Sum the number of credits. 4 + 4 + 3 + 2 = 13, that was a really easy step.
Take the value assigned to the grade and multiply by the number of credits. In our case, it will be:
A * 4 credits = 4.0 * 4 = 16
B * 4 credits = 3.0 * 4 = 12
A * 3 credits = 4.0 * 3 = 12
C * 2 credits = 2.3 * 2 = 4.6
Add all the values. 16 + 12 + 12 + 4.6 = 44.6
Divide the sum by the total number of credits. So for our example it's equal to 44.6/13 = 3.43
The whole weighted average formula may be written as:
(4 * 4 + 4 * 3 + 3 * 4 + 2.3 * 2) / (4 + 4 + 3 + 2) = 3.43
Let's compare this result to an average that is not weighted. Then we don't take the credits into account, and we divide the sum of grades by its total number.
(4 + 3 + 4 + 2.3) / 4 = 3.33
Notice how the weighted average changed. Sometimes it may be a really significant difference - like a grade difference or even whether you pass or fail your course.
Weighted average formula
Let's repeat what the weighted average formula looks like:
weighted-average-formula
But what does it mean? To figure out how to calculate a weighted average, we need to know the weight of each value. Typically, we present the weights in the form of a percentage, or (in statistics) a probability of occurrence. For example, let's suppose that exams, quizzes and homework assignments all contribute to the grade of a class. Each of the three exams is worth 25 percent of the grade, the quizzes are worth 15 percent and the homework assignments are worth 10 percent. To calculate the average you multiply the percentage by the grades and add together. If the test scores are 75, 90, 88, the quiz average is 70, and the homework grade is 86, the weighted average is as follows:
(0.25 * 75 + 0.25 * 90 + 0.25 * 88 + 0.15 * 70 + 0.10 * 86) / 1 = 82.35
Compare this to a non-weighted average of (75 + 90 + 88 + 70 + 86) / 5 = 81.8
In statistics, you will often encounter a discrete probability distribution which has values for x and their associated probabilities. Since the probabilities for each value of x will likely not all be the same, we can apply the weighted average formula. Simply multiply each x value by its probability of occurring and sum the values.
4.5+3+2.7+1.8+4=14
so,14\5=2.8