Difference Between Average and Mean
The term Average is the sum of all the numbers divided by the total number of values in the set. The term Mean is finding of the average of a sample data. Average is finding the central value in math, whereas mean is finding the central value in statistics. We use average when the difference between the values is less, whereas, for the set of values that have more difference, we prefer finding the mean of the data.
|1.||Definition of Average|
|2.||Definition of Mean|
|3.||Difference between Average and Mean|
|6.||FAQs on Difference between Average and Mean|
Definition of Average
By definition, an average is the arithmetic mean of the sum of all the values divided by the total number of values in a given set. An average is calculated for those sets of value which are more or less same. The term average describes the numeric value that represents a large amount of data. An average can be derived by calculating the ratio of the sum of all the values to the number of units or values.
Let us look at an example to understand average better:
Example 1: Find the average of the set of numbers 3, 6, 14, 18, 20, 35, 44
Solution: The formula for finding the average is Sum of the Numbers/Number of Units
Sum of the numbers = 3 + 6 +14 + 18 + 20 + 35 + 44 = 140
Number of units = 7
Therefore, Average = Sum of Numbers/Number of Units
Hence, the average of the set of numbers is 20.
Definition of Mean
A mean is a mathematical term, that describes the average of a sample. In Statistics, the definition of the mean is similar to the average where it is the sum of all the given data values divided by the total number of data values given in the set. A mean is calculated for those sets of values with either more difference or those values that are close to each other. Mean has other forms as well such as the harmonic mean and geometric mean that are used in different situations.
Difference between Average and Mean
Mathematically, average and mean are similar to each other as it is used to explain the set of numbers. Listed below are the key points of average and mean that explain the difference in a table format.
|An Average can be defined as the sum of all numbers divided by the total number of values.||A mean can be defined as an average of the set of values in a sample of data.|
|In other words, an average is also called the arithmetic mean.||Describing the average is called a mean. There 2 other kinds of mean - harmonic and geometric mean.|
|An average is calculated for a set of numbers that are of the same value range.||Mean is mostly used in Statistics where the set of values have a vast difference or they are closely related to each other.|
|An average represents a single number from the list of numbers.||Mean is the central point among the set of numbers.|
|The usage of average is seen in day-to-day life as a conversation in the English language.||The usage of the mean is seen mostly in a technical and mathematical sense.|
|Through the average, we can also find out the values of the median and mode.||On the other hand, the mean does not give the median and mode even though all three - mean, median, and mode, work closely in Statistics.|
- The average of any number series or group is always between its smallest and the largest value.
- Average is used in day-to-day calculations whereas mean is the average is mostly used in statistics while solving math questions.
Solved Examples on Difference between Average and Mean
Example 1: A student has gotten the following grades on his tests: 82, 93, 79, and 69. He wants a 75 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?
We need to find out the minimum grade by adding all the grades given and divide it by the number of grades. Since we don't have a score for the last test, let's use the variable 'x' to determine the average.
(82 + 93 + 79 + 69 + x)/5 = 75
We move the five to the other side and multiply 5 with 75.
82 + 93 + 79 + 69 + x = 375
323 + x = 375
x = 375 - 323
x = 52
Hence, the student needs to score at least a 52 on the last test.
Example 2: Find the mean for the following data: 45, 76, 2, 10, 33.
The given list is 45, 76, 2, 10, 33
Mean = Sum of observations/Total number of observations
= (45 + 76 + 2 + 10 + 33)/ 5
Therefore, the mean for the following list is 33.2
FAQs on Difference between Average and Mean
What is the Difference Between Mean and Average?
Average, also called the arithmetic mean, is the sum of all the values divided by the number of values. Whereas, mean is the average in the given data. In statistics, the mean is equal to the total number of observations divided by the number of observations.
How do you Calculate Mean vs Average?
The mean is the average of the numbers and to calculate both average and mean we need to add up all the values, then divide by the total number of values. In other words, it is the sum of the values divided by the count of the values. The formulas for both are more or less the same. Average = Mean = Sum/Count
Does Average Always Reciprocates as Mean?
Since both average and mean are similar, yes average usually does reciprocate as mean. Average is also called that arithmetic mean and mean is the average of the sample data.
What is the Formula for the Average?
Average = Sum of the Observations/Number of Observations. For example, the average of 2,5,7,9, and 7 is 30 divided by 5 which is 6