In mathematics, the mean is defined as the average of a set of numbers. In statistics, means is considered as the measure of central tendencies. Median is defined as the middle number when the set of numbers is sorted in ascending or descending order. Mode is the statistical method that refers to the value that repeats the maximum number of times.
Mean gives the central value of the set of values. There are different types of means that are,
- Arithmetic Mean
- Geometric Mean
- Harmonic Mean
Arithmetic mean
Arithmetic mean is the most often used method to find a mean or average. It is calculated by taking a sum of a set of numbers and dividing it by the count of the numbers in the set. It is used when all the values in the given data have the same unit of measurement such as all the given numbers are heights, miles, hours, etc. For example, consider numbers 4, 7, 9, and 10. The sum of the numbers is 30 and the count of numbers is 4. The arithmetic mean of the numbers is 30 divided by 4 or 7.5.
There are also other different types of means such as geometric mean and harmonic mean and it is used to calculate the economic data in various other situations in finance and investing.
- The geometric mean is defined as the average value of a given set of numbers by multiplying them. The numbers are multiplied altogether and the nth root of the multiplied number is taken.
- The harmonic mean is defined as the numerical average and it is calculated by dividing the number of observations by the reciprocal of each number in the series.
In finance, arithmetic mean is not an appropriate method to calculate an average when there are a lot of numbers to count and a single count can change the mean by a large amount.
Where do we use the arithmetic mean?
Arithmetic mean is taken out for the sequences that are arithmetic sequences. The arithmetic mean is the easiest and most widely used measure to calculate the mean. The following are some of the important applications of arithmetic mean,
- It is used in algebraic treatment.
- It is used to calculate the average score in sports such as cricket.
- It is also used in many diverse fields i.e.’ economics, anthropology, and history.
- It is also used to measure the average temperature of the earth to measure global warming.
- It is also used to measure the annual rainfall of a particular area.
Limitation of the Arithmetic Mean
Consider that there are 10 people and the salary of 9 of them is between 30 to 35 k per month and the tenth one has a salary of 120 k. The mean salary of these 10 people does not represent the salary of the group. In this case, the average is calculated by the median of the salaries of the people.
Steps to calculate Arithmetic Mean
- Count the number of values in the set.
- Add all the values together.
- Divide the sum by the number of values in the set to obtain the arithmetic mean.
- Make sure the calculation is correct.
Sample Problems
Question 1: Calculate the arithmetic mean of the given numbers: 25, 20, 32, 45, 33, 37, and 40?
Solution:
Given that, the numbers are 25, 20, 32, 45, 33, 37 and 41.
Step 1
The count of numbers is 7.
Calculate the sum of the given numbers.
25 + 20 + 32 + 45 + 33 + 37 + 41 = 231
Step 2
Calculate the arithmetic mean of the given numbers.
231/7 = 33
Hence, the arithmetic mean of the given numbers is 33.
Question 2: Calculate the arithmetic mean of the given numbers: 323, 342, 400, 389, 360, 327, 389, and 352.
Solution:
Given that, the numbers are 323, 342, 400, 389, 360, 327, 389, and 352.
Step 1
The count of numbers is 8.
Calculate the sum of the numbers.
323 + 342 + 400 + 389 + 360 + 327 + 389 + 350 = 2880
Step 2
Calculate the arithmetic mean of the given numbers.
2880/8 = 360
Hence, the arithmetic mean of the given numbers is 360.
Question 3: Calculate the arithmetic mean of the given numbers: 2.5, 4.8, 2.7, 6.0, 3.1, 6.4, 7.2, 8.2, and 5.5.
Solution:
Given that, the numbers are 2.5, 4.8, 2.7, 6.0, 3.1, 6.4, 7.2, 8.2, and 5.5.
Step 1
The count of numbers is 8.
Calculate the sum of the numbers.
2.5 + 4.8 + 2.7 + 6.0 + 3.1 + 6.4 + 7.2 + 8.2 + 5.5 = 56.4
Step 2
Calculate the arithmetic mean of the given numbers.
56.4/8 = 5.8
Hence, the arithmetic mean of the given numbers is 5.8