The two terms – “frequency” and “average” refer to two different concepts. The word frequency can never be used as a substitute for average. In this article, we explain the difference between the two words and show how they are different by looking at examples.

**Definition of Frequency:**

The word “frequency” refers to the number of times a given data value occurs in a data set. For example, consider the following set of 10 data values: 1, 1, 1, 1, 3, 3, 5, 5, 5, 7

Here, the data value 1 occurs exactly 4 times, therefore the frequency of the data value 1 is equal to 4.

Similarly, the frequency of the data value 3 is equal to 2. The frequency of the data value 5 is equal to 3. On the other hand, the frequency of the data value 7 is equal to 1 since it occurs exactly once in the given data set. We can summarize this information in the form of a frequency distribution table.

Data Values | Frequency |

1 | 4 |

3 | 2 |

5 | 3 |

7 | 1 |

It is very convenient to count the frequencies of the data values and express the data in the form of a frequency distribution table as above. This is because if we are given a large number of data values then it can be very difficult to grasp the data by looking at the individual data points. It is much more convenient to look at the frequency distribution table which expresses the data in a compactified form.

**Definition of Average:**

The idea behind an average is to represent the given data set by a single value that represents that data set. The average refers to the central value of the data set. The average is also known as the mean. It can be calculated using the following formula,

Mean = \frac{\text{Sum of Observations}}{\text{Number of Observations}}Let us once again look at the example considered above. Consider the following set of data values,

1, 1, 1, 1, 3, 3, 5, 5, 5, 7The average can be calculated using the above formula, Mean = \frac{1 + 1 + 1 + 1 + 3 + 3 + 5 + 5 + 5 + 7}{10} = \frac{32}{10} = 3.2

**Difference Between Average and Frequency:**

The above two definitions make clear the difference between the concept of average and the concept of frequency. While the concept of frequency is about counting how many times a data value occurs in a data set, the concept of average is all about representing the given data values by a single representative number known as the average. The two words should never be used to mean the same thing.