The term average Is used to refer to the average number of a set of numbers.
In general, the average is calculated by summing all the figures or values presented and dividing them by the total amount of values.
For example:
Values: 2, 18, 24, 12
Sum of values: 56
Division between 56 (Sum of values) and 4 (Total amount of values): 14
Average = 14
In statistics, the average is used to reduce the amount of data that the statesman must manipulate, so that the work is easier. In this sense, the average is a synthesis of the data collected.
In this discipline, the term"average"is used to refer to different types of media, the main being the arithmetic mean and the weighted average.
The arithmetic mean is the one that is calculated when all the data have the same value or importance in the eyes of the statesman.
On the other hand, the weighted average is the one given when the data do not have the same importance. For example, exams that are worth different note.
Arithmetic average
The arithmetic mean is a type of position mean, which means that the result shows the centralization of the data, the general trend of these.
This is the most common type of average of all and is calculated as follows:
Step 1: The data to be averaged are presented.
For example: 18, 32, 5, 9, 11.
Step 2: They add up.
For example: 18 + 32 + 5 + 9 + 11 = 75
Step 3: The amount of data to be averaged is determined.
For example: 6
Step 4: The result of the sum is divided by the amount of data to be averaged and that will be the arithmetic mean.
For example: 75/6 = 12, 5.
Examples of calculation of arithmetic mean
Example # 1 arithmetic mean
Matt wants to know how much money he has spent on average each day of the week.
On Monday I spent $ 250.
On Tuesday he spent $ 30.
He did not spend anything on Wednesday.
On Thursday he spent $ 80.
On Friday he spent $ 190.
Saturday spent $ 40.
On Sunday he spent $ 135.
Values to be averaged: 250, 30, 0, 80, 190, 40, 135.
Total number of values: 7.
250 + 30 + 0 + 80 + 190 + 40 + 135 = 725/7 = 103, 571428571
On average, Matt spent $ 103.571428571 every day of the week.
Example # 2 arithmetic mean
Amy wants to know what her average is at school. His notes are as follows:
In literature: 20
In English: 19
In French: 18
In arts: 20
In history: 19
In chemistry: 20
In physics: 18
In Biology: 19
In Mathematics: 18
In sports: 17
Values to be averaged: 20, 19, 18, 20, 19, 20, 18, 19, 18, 17.
Total amount of values to be averaged: 10
20 + 19 + 18 + 20 + 19 + 20 + 18 + 19 + 18 + 17 = 188/10 = 18.8
Amy's average is 18, 8 points.
Example # 3 of arithmetic mean
Clara wants to know what her average speed is by running 1000 meters.
Time 1 - 2, 5 minutes
Time 2 - 3,1 minutes
Time 3 - 2,7 minutes
Time 4 - 3.3 minutes
Time 5 - 2.3 minutes
Values to be averaged: 2, 5 / 3,1 / 2,7 / 3,3 / 2,3
Total number of values: 5
2.5 + 3.1 + 2.7 + 3.3 + 2.3 = 13.9 / 5 = 2.78.
Clara's average speed is 2, 78 minutes.
Weighted average
The weighted average, also known as a weighted arithmetic mean, is another type of position average (which seeks to obtain a centralized data).
This differs from the arithmetic mean because the data to be averaged do not have the same importance, so to speak.
For example, school assessments have different weights. If we want to calculate the average of a series of evaluations, the weighted average should be applied.
The weighted average is calculated as follows:
Step 1: Identify the figures to be weighted together with the value of each.
For example: A test that is worth 60% (in which 18 points were obtained) and a test that is worth 40% (in which 17 points were obtained).
Step 2: Multiply each of the numbers with their respective value.
For example: 18 x 60 = 1080 // 17 x 40 = 680
Step 3: Add the data obtained in step 2.
For example: 1080 + 680 = 1760
Step 4: The percentages that indicate the value of each of the numbers are added together.
For example: 60 + 40 = 100
Step 5: The data obtained in step 3 is divided by the percentage.
For example:
1760/100 = 17.6
Example of the weighted mean calculation
Hector has presented a series of chemistry exams and wants to know what his average.
Exam n ° 1: 20% of the total grade. Hector got 18 points.
Exam 2: 10% of the total grade. Hector got 20 points.
Exam 3: 15% of the total grade. Hector got 17 points.
Exam 4: 20% of the total grade. Hector got 17 points.
Exam 5: 30% of the total grade. Hector got 19 points.
Exam n ° 6: 5% of the total grade. Hector got 20 points.
Values:
Data # 1
18 x 20 = 360
20 x 10 = 200
17 x 15 = 255
17 x 20 = 340
19 x 30 = 570
20 x 5 = 100
Sum: 1825
Data # 2
20% + 10% + 15% + 20% + 30% + 5% = 100%
Average
1825/100 = 18.25
Hector's average in chemistry was 18, 25 points.
References
- Average. . How to calculate average. Downloaded on August 1, 2017, from statisticshowto.com
- How to calculate mean value. Retrieved on August 1, 2017, from mathisfun.com
- How to calculate the mean or average. Retrieved on August 1, 2017, from thoughtco.com
- Math Help. How to calculate an Average. Retrieved on August 1, 2017, from youtube.com
- Calculating average. Retrieved on August 1, 2017, from khanacademy.org
- How to calculate average. Retrieved on August 1, 2017, from wikihow.com
- Weighted average. Retrieved on August 1, 2017, from investopedia.com
- How to calculate weighted average. Retrieved on August 1, 2017, from sciencing.com.