Weighted average calculator
Using the explanations and examples below, you can easily explain to your child how to calculate an average.
The average of 2 numbers
The average of 2 numbers is essentially the number that lies exactly in the middle of the two numbers on the number line.
Draw a number line with 2 numbers and have your child determine what lies exactly in the middle by taking leaps.
Next, demonstrate that you can also calculate this middle, the average, by adding 28 and 50 together and then dividing the result by 2:
28 + 50 = 78
78 / 2 = 39
Another way to show it:
In this example, Mark has 2 candies, and John has 4. How many candies would they have if they both had the same amount?
To figure it out, you need to add everything together and then distribute it evenly:
2 + 4 = 6 candies
6 candies / 2 = 3 candies
If the amounts were equal, they would both have 3 candies.
That is essentially what the average is: the number you get when you add all the amounts together and then distribute them "fairly."
Calculating the average of 3 or more numbers
Once your child understands this concept, you can move on to calculating the average of 3 or more numbers.
You can do this with candies too:
Julie and Melissa each have 5 candies, but Vincent has only 2. They decide to divide them fairly.
So, they add everything together and then divide it by 3:
5 + 5 + 2 = 12 candies
12 candies / 3 = 4 candies
The average of 5, 5, and 2 is 4.
To calculate the average, add all the numbers together and then divide by the number of values.
What is the average grade of the group?
Come up with some more examples like this, or better yet, let your child come up with them.
In school, calculating averages in word problems is sometimes combined with other types of problems.
For example:
The 5th grade took a test.
5 children got a 9;
4 children got an 8;
3 children got a 7;
8 children got a 6
and 2 children got a 5.
What is the average grade of the children?
Solution:
First, you need to calculate how many points all the children scored in total.
5 children got a 9, so 5 x 9 = 45 points in total
4 children got an 8, so 4 x 8 = 32 points in total
3 children got a 7, so 3 x 7 = 21 points in total
8 children got a 6, so 8 x 6 = 48 points in total
2 children got a 5, so 2 x 4 = 8 points in total
Together they scored 45 + 32 + 21 + 48 + 8 = 154 points.
Then that number needs to be divided by the number of children.
There are 5 + 4 + 3 + 8 + 2 = 22 children.
154 ÷ 22 = 7.
The average grade is 7.
Calculating the average with a 0 included
There are also exercises where one of the numbers being added is 0.
For example:
On Monday, Tuesday, and Thursday, the farmer sells 8 eggs.
On Wednesday, he doesn't sell any eggs, and on Friday, he sells 6.
How many eggs did he sell on average per day that week?
Many children eagerly write down:
Monday 8, Tuesday 8, Thursday 8, Friday 6, so a total of 30 eggs in 4 days is 7.5 eggs per day.
But the question was how many eggs he sold on average per day that week.
And Wednesday should be included. Therefore, the total should be divided by 5 days.
In such cases, children often forget to include the 0 eggs from Wednesday.
Let's go back to the example of Julie, Melissa, and Vincent:
Julie and Melissa each have 3 candies. Then Vincent joins, and he doesn't have any candies. They decide to share equally:
3 + 3 + 0 = 6
6 / 3 = 2
When calculating the average, you must divide the total by the number of values. If you don't include Vincent's 0 candies, you would get:
3 + 3 = 6
6 / 2 = 3
But then Vincent still has nothing! That's why the 0 must be included because it affects the correct number of values you're dividing by.
Splitting the bill
For example:
Lori, Tom, and Sean are going out together.
Lori pays for the food, which is $24.00.
Tom pays for the cinema, which is $36.00.
And Sean pays for the popcorn, which is $12.60.
They decide to split the costs equally. How much does each person have to pay? Who owes money to others, and how much?
Solution:
The total spent is $24.00 + $36.00 + $12.60 = $72.60.
Since there are three of them, the evening cost $72.60 / 3 = $24.20 per person.
So Lori owes $0.20 to Tom, and Sean owes $11.60.
In this exercise, the amounts need to be added together and then divided by the number of people. Essentially, you're calculating the average, but here it's described as splitting the bill.
Returning to averages with a 0 included:
If there was a fourth person who didn't pay anything, the total amount would need to be divided by 4. So, the 0 still matters! Your child may find this logical in this situation, but when it comes to more abstract topics, like the average amount of rainfall in a week, they might not find it as intuitive. They may struggle to understand that a day without rain, 0 mm, still counts in the average.
Calculating weighted average
The weighted average takes into account the "weight" of the numbers. The size of the weighting factor determines the extent to which the number is included in the average. The weighted average is most affected by the numbers with the largest weighting factor. For example, an exam will have a higher weighting factor and therefore more influence than a written assignment in determining the overall report grade.
The weighted average is an average of a group of numbers, where each number has a certain weighting factor. You calculate the weighted average by multiplying each number by its weighting factor. Then, you divide the sum of all these products by the sum of the weighting factors. The formula for the weighted average is as follows:
weighted average = ((weighting factor x value) + (weighting factor x value) + (weighting factor x value)) / total weighting factors
For example, in high school, the grades obtained in a written assignment are not weighted as heavily as the grades for the exams. If you get a 4 for the assignment and a 7 for the exam, the exam grade usually counts double. Therefore, you pretend you got 2 times a 7 and calculate the average of 4, 7, and 7. Then you divide 18 by 3, and your average grade is 6.
Calculating average speed
Calculating average speed is a special case of weighted average. The weighting factor consists of the time or distance at which a given speed is maintained.
Let's use an example to make this clear:
The Parker family is visiting their grandmother.
First, they drive at 30 MPH on the street for 10 minutes.
Then, in the village, they drive at 50 MPH for 20 minutes.
Finally, on the highway, they drive at 100 MPH for 30 minutes.
What is the average speed?
Average speed = ((30*10) + (50*20) + (100*30)) / (10 + 20 +30) = 71 MPH.