Is defined as the sum of the values of the variables divided by the number of observations?

Average and mean are similar yet are different. 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.

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

= 140/7

= 20

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.

Related Topics

Listed below are a few topics related to the difference between average and mean, take a look.

• Mean, Median and Mode
• Arithmetic Mean
• Statistics

Important Points

• 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 that is mostly used in statistics while solving math questions.

Examples on Difference between Average and Mean

1. 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?

   Solution:

   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.

2. Example 2: Find the mean for the following data: 45, 76, 2, 10, 33.

   Solution:

   The given list is 45, 76, 2, 10, 33

   Mean = Sum of observations/Total number of observations

   = (45 + 76 + 2 + 10 + 33)/ 5

   = 166/5

   = 33.2

   Therefore, the mean for the following list is 33.2

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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 averages 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.

Why is Average Called Mean?

A mean can be defined as an average of the set of values in a sample of data. An average is referred to as the sum of all values divided by the total number of values. In mathematics, both the words mean and average are related but have their own difference as mentioned in this article.

Are Mean and Average Interchangeable?

Yes, most often average and mean are used interchangeably. In Statistics, instead of using the word average, the word mean is used. It does tend to create confusion as the basic meaning of both the words average and mean are the same.

What is the sum of all the observations divided by the number of observations?

Is defined as the sum of all items divided by their number?

What is the total number of observations?

How do you find the sum of observations?