**Mean** is a measure of central tendency and is considered to be a very important parameter of statistics. Mean or Average is the sum of the data sets or numbers or values divided by the number of numbers or data sets or values.

**What is a discrete number?**

A discrete number is a standalone number. It might be a whole number or fractional number but it stands on its own with no extension or range. An example of a discrete number is 5, 12, 10.6, 17, 20

**What is a continuous number?**

A continuous number is a range of numbers packaged as a single entity. An example of a continuous number is 5 – 10, 20 – 30, 25 – 50.

There are two possibilities in calculating the mean of a set of discrete numbers. One can either compute the mean via the application of frequency or no frequency at all.

For Example: A set of discrete numbers such as these:

4, 5, 6, 7, 8, 9

These numbers all occur once and have a frequency of 1 per number.

Therefore, if you want to create a table for the number and frequency, it looks like this:

**Number **4, 5, 6, 7, 8, 9

**Frequency **1, 1, 1, 1, 1, 1

You can clearly see that there is no need for applying frequency to calculate the mean of the above set of numbers. Application of frequency on a large set of numbers makes it easier to organize and compute the mean.

Now, for a set of numbers such as these:

4, 4, 4, 2, 4, 5, 3, 3, 3, 2, 1, 1, 6, 4, 3, 2, 4, 2, 5, 2, 1

You can see that some of the discrete numbers occur more than once and this implies that application of frequency is useful and makes the computing of mean easier and comprehensive.

From the display of numbers above you can see that the number 4 occurred **6 **times, the number 2 occurred **4 **times, the number 5 occurred **2** times, the number 3 occurred **4** times, the number 1 occurred **3** times, the number 6 occurred **1** time.

Arranging the values in the form of a table gives us:

**Number **4, 2, 5, 3, 1, 6

**Frequency ** 6, 4, 2, 4, 3, 1

Today, I would like for us to start with how to compute the mean of a set of discrete numbers without frequencies.

Let’s say we are given a set of numbers such as 4, 5, 2, 1, 8 and our task is to find the mean or average of these numbers.

**What do we do?**

- First, we add all the numbers together, obtaining the sum
- Next, we divide the sum by the number of the numbers (N) given

**Obtaining the sum**

sum = 4 + 5 + 2 + 1 + 8

sum = 20

The total number of numbers is **5.**

Now, dividing the sum by total number of numbers (N) gives us the **mean** or **average**.

Mean or Average = 20 / 5

Mean or Average = 4

Therefore, the mean or average of 4, 5, 2, 1, 8 set of numbers is **4**.

Now, let us try to calculate the mean of a set of discrete numbers with frequencies.

For Example:

Given these set of numbers 4, 4, 4, 2, 4, 5, 3, 3, 3, 2, 1, 1, 6, 4, 3, 2, 4, 2, 5, 2, 1 organize them into frequency and compute the mean.

Organizing the above set of numbers is easy and has been well explained above

Therefore, the Number – Frequency table looks thus:

**Number **4, 2, 5, 3, 1, 6

**Frequency ** 6, 4, 2, 4, 3, 1

**How do we compute the mean or average?**

- First, we multiply the discrete number by the corresponding frequency individually
- Second, we sum up the products to give the
**sum** - Third, we add up the frequencies to obtain the total number of numbers (N)
- Lastly, we divide the sum by the total number of numbers (N)

Now, lets compute a **Number-Frequency-Product** table

**Number **4, 2, 5, 3, 1, 6

**Frequency ** 6, 4, 2, 4, 3, 1

**Product **24, 8, 10, 12, 3, 6

Sum of the product is 28 + 8 + 10 + 12 + 3 + 6 which results to **67**.

Sum of the frequencies 6 + 4 + 2 + 4 + 3 + 1 which results to **20**.

Therefore, the **mean** or **average** of these set of numbers is 67 / 20 which results **3.35**.

**Computing Mean or Average for Continuous Numbers**

For Example:

Compute the **average** of a continuous numbers: 31 – 40, 41 – 50, 51 – 60 with frequencies 2, 3, 4 respectively

**How do we compute this mean?**

- First, we compute the individual mean of each of the continuous numbers
- Then, multiply the mean of the continuous number by its corresponding frequency.
**ADD UP**the products from*step two*to get the**sum of the products****ADD UP**the frequencies, to get the sum of frequencies- Lastly, divide the sum of the products by the sum of frequencies

To get the individual mean of a continuous number is very simple. For Example: a continuous number such as 31 – 40. You do (31 + 40) / 2. This results to 71 / 2 which finally comes up to **35.5**.

Therefore,

31 – 40 is represented by **35.5**

41 – 50 is represented by **45.5**

51 – 60 is represented by **55.5**

**Table Representation**

**Number** 31 – 40, 41 – 50, 51 – 60

**Frequency **2, 3, 4

**m **35.5 45.5 55.5

Now, compute the product of **m **(individual mean of the continuous number) and the frequency which means: 35.5 x 2, 45.5 x 3, 55.5 x 4 respectively. **f.m **represents the product.

**Number** 31 – 40, 41 – 50, 51 – 60

**Frequency **2, 3, 4

**m **35.5, 45.5, 55.5

**f.m **71, 136.5, 222

Now, take the sum of the product of the frequency and individual mean of the continuous numbers respectively as follows: 71 + 136.5 + 222 which results **429.5**. The sum of the frequencies, 2 + 3 + 4 which results to **9**.

Therefore, the **mean or average** of the set of continuous numbers is sum of the product of the frequency and individual mean of the continuous numbers divided by the sum of frequencies which results to **429.5 / 9** which is **47.72**.

I hope you had a nice lesson today learning how to solve and calculate the mean or average of a set of discrete and/or continuous numbers.

Below is a video of how **Nickzom Calculator – The Calculator Encyclopedia** calculates and solves mean or average for both discrete and continuous numbers with steps. Watch and Enjoy!

You can access **Nickzom Calculator** (The Calculator Encyclopedia) via any of these channels:

Web – https://www.nickzom.org/calculator-plus

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Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8