Definition of Average and Mean
The average is the sum of all values in the set divided by the number of values. It is also called the arithmetic mean.
For example, if we have a set of numbers 2, 4, 6, and 8, the sum of these numbers is 20, and since there are four numbers, the average would be 20/4 = 5.
The mean is another way to find the central of a set of data. It is the value that defines the middle of the data when the values are arranged in order. To find the mean, we add up all the values in the set and divide by the number of values.
For example, if we have a set of numbers 3, 7, 9, 10, and 12, the sum of these numbers is 41, and since there are five numbers, the mean would be 41/5 = 8.2.
What is the Difference Between Average and Mean?
The average and mean are both used to describe the center of a set of data. Here are given below the main differences between average and mean:
| Average | Mean |
|---|---|
| Also known as arithmetic mean | Also known as statistical mean |
| Calculated by summing all values and dividing by the number of values | Calculated by finding the middle value of the data when arranged in order |
| Can be affected by extreme values (outliers) in the dataset | Not affected by extreme values (outliers) in the dataset |
| Suitable for evenly distributed data | Suitable for normally distributed data |
| May not represent the actual values in the dataset | Represents an actual value in the dataset |
| Can be used for discrete and continuous data | Can be used for continuous data only |
Solved Examples
Example 1: What is the average and mean score of test scores: 85, 90, 92, 78, 87?
To find the average, we add up all the scores and divide by the number of scores: (85 + 90 + 92 + 78 + 87) / 5 = 86.4
To find the mean, we arrange the scores in order: 78, 85, 87, 90, 92 The middle value is 87, so the mean score is 87.
Therefore, the average score is 86.4 and the mean score is 87.
Example 2: Suppose you have the following dataset representing the monthly salaries of employees in a company: $3000, $3500, $4000, $4500, $5000. What is the average and mean salary?
To find the average, we add up all the salaries and divide by the number of employees: (3000 + 3500 + 4000 + 4500 + 5000) / 5 = $4000
To find the mean, we arrange the salaries in order: $3000, $3500, $4000, $4500, $5000 The middle value is $4000, so the mean salary is $4000.
Therefore, the average salary is $4000 and the mean salary is also $4000.
Example 3: What is the average and mean age if the ages of 10 people: 18, 20, 22, 25, 28, 30, 35, 40, 45, 50?
To find the average, we add up all the ages and divide by the number of people: (18 + 20 + 22 + 25 + 28 + 30 + 35 + 40 + 45 + 50) / 10 = 31.3
To find the mean, we arrange the ages in order: 18, 20, 22, 25, 28, 30, 35, 40, 45, 50 The middle value is the average of the two middle values, which is (28 + 30) / 2 = 29.
Therefore, the average age is 31.3 and the mean age is 29.
Frequently Asked Questions – FAQs
Q: Is average the same as mean?
A: Yes, average and mean are often used interchangeably and refer to the same concept of calculating the central tendency of a set of data.
Q: How do I know whether to use the average or the mean?
A: The choice between the two will depend on the type of data and the purpose of the analysis. The average is more commonly used and is suitable for evenly distributed data, while the mean is suitable for normally distributed data.
Q: Can outliers affect the average and mean?
A: Yes, outliers can affect the average but not the mean. The average is calculated by summing all values and dividing by the number of values, so if there are extreme values in the dataset, they can significantly affect the result. However, the mean is calculated by finding the middle value of the data when arranged in order, so extreme values have no effect.
Q: Can average and mean be used for both discrete and continuous data?
A: Yes, average and mean can be used for both discrete and continuous data. However, the mean is more commonly used for continuous data, while the average is used for both discrete and continuous data.