What is the sum of the data values divided by the number of data values in the set this is also called the average?

Though we commonly use the word average in everyday life when discussing the number that’s the most “typical” or that’s “in the middle” of a group of values, more precise terms are used in math and statistics. Namely, the words mean, median, and mode each represent a different calculation or interpretation of which value in a data set is the most common or most representative of the set as a whole.

In this article, we’ll answer these questions and more:

• Is there a difference between mean and average?
• What’s the difference between mean, median, and mode?
• How do you find the mean, median, and mode?

You find the mean (informally called the average) by adding up all the numbers in a set and then dividing by how many values there are. When you arrange a set of values from smallest to largest, the median is the one in the middle. The mode is simply the value that occurs the most in the set.

mean vs. average

In math, the word mean refers to what’s informally called the average. They mean the same thing, but in the context of math and statistics, it’s better to use the word mean to distinguish from other things that might be casually referred to as “average” values in a general sense (meaning values that are the most representative or common within the set).

What is the mean, median, and mode?

The mean is the number you get by dividing the sum of a set of values by the number of values in the set.

In contrast, the median is the middle number in a set of values when those values are arranged from smallest to largest.

The mode of a set of values is the most frequently repeated value in the set.

To illustrate the difference, let’s look at a very simple example.

Here’s an example set of seven values: 2, 3, 3, 4, 6, 8, 9.

To find the mean: add up all the values (2+3+3+4+6+8+9=35) and then divide that total by the number of values (7), resulting in a mean of 5. This is what most people are referring to when they refer to the average of some set of numbers.

To find the median: find the value that’s sequentially in the middle. In a set of seven numbers arranged in increasing value, the median is the fourth number (since there are three before and three after). In this set (2, 3, 3, 4, 6, 8, 9), the median is 4. When a set has an even number of values, the median is the mean of the two middle values (in other words, you find the median by adding the two middle numbers together and dividing by two).

To find the mode: simply look to see which value shows up the most. In the example set, the mode is 3, since it occurs twice and all the other values occur only once.

Of course, this set of values is very simple compared to data sets you’re likely to encounter in real life. In cases when there is too much data to look at all at once, there are often special tools (such as those used in spreadsheet software) that you can use to determine the mean, median, and mode.

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.

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

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.