The term average is used to refer to the average number of a set of numbers. In general, the average is calculated by adding all the figures or values presented and dividing them by the total number of values.
For example:
Values: 2, 18, 24, 12
Sum of the values: 56
Division between 56 (sum of the values) and 4 (total number of values): 14
Average = 14
In statistics, the average is used to reduce the amount of data that the statistician must manipulate, so that the work is easier. In this sense, the average represents a synthesis of the data collected..
In this discipline, the term “average” is used to refer to different types of average, the main ones 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 statistician. For its part, the weighted average is the one that occurs when the data do not have the same importance. For example, exams that are worth different marks.
The arithmetic mean is a type of position average, 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: Determine the amount of data to average.
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.
Matt wants to know how much money he has spent on average each day of the week.
Monday I spend $ 250.
On Tuesday he spent $ 30.
On wednesday he didn't spend anything.
On Thursday he spent $ 80.
On Friday he spent $ 190.
On Saturday he spent $ 40.
On Sunday he spent $ 135.
Average values: 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 each weekday.
Amy wants to know what her GPA 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 math: 18
In sports: 17
Values to average: 20, 19, 18, 20, 19, 20, 18, 19, 18, 17.
Total number of values to average: 10
20 + 19 + 18 + 20 + 19 + 20 + 18 + 19 + 18 + 17 = 188/10 = 18.8
Amy's average is 18.8 points.
Clara wants to know what her average speed is when 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
Average values: 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.
The weighted average, also known as weighted arithmetic average, 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 you want to calculate the average of a series of evaluations, you must apply the weighted average.
The calculation of the weighted average is carried out as follows:
Step 1: The figures to be weighted are identified along with the value of each one.
For example: An exam worth 60% (in which 18 points were obtained) and an exam that is worth 40% (in which 17 points were obtained).
Step 2: Each of the figures is multiplied with its respective value.
For example: 18 x 60 = 1080 // 17 x 40 = 680
Step 3: The data obtained in step 2 are added.
For example: 1080 + 680 = 1760
Step 4: The percentages that indicate the value of each of the figures are added.
For example: 60 + 40 = 100
Step 5: Divide the data obtained in step 3 by the percentage.
For example:
1760/100 = 17, 6
Héctor has taken a series of chemistry exams and wants to know what his GPA is.
Exam n ° 1: 20% of the total mark. Héctor obtained 18 points.
Exam n ° 2: 10% of the total mark. Héctor obtained 20 points.
Exam 3: 15% of the total mark. Héctor obtained 17 points.
Exam n ° 4: 20% of the total mark. Héctor obtained 17 points.
Exam n ° 5: 30% of the total mark. Héctor obtained 19 points.
Exam n ° 6: 5% of the total mark. Héctor obtained 20 points.
Values:
Facts # 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
Facts # 2
20% + 10% + 15% + 20% + 30% + 5% = 100%
Average
1825/100 = 18, 25
Hector's average in chemistry is 18, 25 points.
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