Home How to Solve and Calculate the Mean or Average of Discrete and Continuous Numbers

How to Solve and Calculate the Mean or Average of Discrete and Continuous Numbers

Finding the mean or average of discrete and continuous numbers is a fundamental aspect of mathematics and data analysis. Whether dealing with discrete values like counts or continuous data such as measurements, understanding the process of calculating the mean or average is crucial. In this article, we’ll explore step-by-step methods to solve and calculate the mean or average, demystifying both discrete and continuous scenarios for clearer statistical insights.

What is a Mean?

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.

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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.

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