Many people didn't like math when they were in school. Most of them thought, “You don’t use this in everyday life!” Unfortunately, this is wrong because almost everything in this world is made with the help of mathematics. In addition, if you want to build a structure, professionals use this knowledge to make calculations to determine whether it can be built and is safe to use. For example, experts in the building industry are using the frequency density formula to find the best concrete mixture.
When you are creating a building, planning involves multiple math calculations. You have to measure the length, area, volume, and angle to know how many materials you need and how much it will cost. For example, an easy task such as pouring concrete for the road. You can apply the equations to know the volume, estimate how many truckloads you need, how much waste it is going to be, and how much it will cost. Moreover, involving geometry, estimation, and multiplication for one task.
This shows how math has a key role in this sector. Furthermore, one of the formulas that is usually used is the frequency density formula. In this article, you are going to learn how this equation can help construction workers build a safe building while meeting the quality and aesthetics.
What is the formula for relative frequency density?
The frequency density formula is a method that uses dividing the frequency by the class width. Doing so will help show the rate distribution. This is used to show an accurate histogram. The higher the rate, the larger the area of the bar on a histogram. The formula will be shown as this:
The purpose of the frequency density formula is to show data in a histogram when the group sizes are not the same. For example, if one group has a range of 0-20 and another one has a narrower range, like 21-30, using the regular equation will be unfair. Through frequency density, the formula helps to adjust for the width and create a balanced result.
Moreover, it is not only about how much data is in a group but also how packed the data is within each class. The higher the density, the more information in a smaller range. In other words, the group is tighter. This frequency density formula will show a fair comparison across different group sizes and create the correct shape for the histogram.
The role of frequency density formula in the construction sector
Building a structure is not only about hammer and nails. Above all, you are going to need data analysis in planning. This will support your decision-making, improve safety, and increase efficiency. The frequency density formula enables you to create images on a drawing, so workers can use that as a guide in executing the plan. As a result, it will review and calculate structural problems to make sure the building is safe.
Furthermore, it has plenty of practical uses in the field. People who work in engineering and quality control often use this method to support their work. The frequency density formula provides many benefits for building structures, such as:
Quality control of materials
If you are planning to make a structure, you need to choose which materials that fit and meet the standards. The frequency density formula guides you in measuring strength, ranges, thickness, and more in materials. They can be grouped into intervals of different widths. As a result, you can choose the part that fits your needs effectively.
|
Strength (MPa) |
Frequency |
Width (MPa) |
Frequency Density |
|
11-15 |
2 |
5 |
0.4 |
|
16-20 |
10 |
5 |
2.0 |
|
21-25 |
12 |
5 |
2.4 |
|
26-40 |
16 |
15 |
1.07 |
For example, you are currently testing 40 concrete samples. You grouped those items by compressive strength. The minimum strength you are looking for is 21-25 MPa. As you can see, most of the groups have a 5 MPa wide gap, except for the 25-40 MPa (15 MPa). From this table, you can conclude that even though the 26-40 MPa group has the most samples, it doesn’t have the most frequency density (1.07). The one with the highest density is 21-25 MPa (2.4 MPa). With this, there are too many samples that are too close to the minimum required strength.
Land surveying
Before you build a structure, you need to conduct a land survey or soil testing. The frequency density formula can help you see the physical and chemical properties in the soil and look for potential issues that can affect the stability and sustainability of the building. When you are testing it, you are going to need data about soil depth, density, or moisture at different depths.
|
Depth range (m) |
Frequency |
Width (m) |
Frequency Density |
|
0-1 |
6 |
1 |
6.0 |
|
1-3 |
9 |
2 |
4.5 |
|
3-6 |
12 |
3 |
4.0 |
|
7-10 |
8 |
4 |
2.0 |
To illustrate, you want to measure the moisture content at different soil depths with the data from the table above. The higher the frequency, the more moisture it has. Although the table says the 3-6 m group has the most samples, it doesn’t have the most frequency density (4.0). This is because it has a wider range, so it becomes less dense. The one that has the most moisture is the 0-1 m with 6.0 frequency density. The frequency density formula helps to conclude that the top layers hold more moisture and become valuable information for engineers.
Construction planning
Planning is crucial if you want to construct a building. There are many things you have to consider, such as materials, workforce, costs, and many more. You have to estimate timelines, schedule the workers and equipment, manage costs, look for risks and delays, and also monitor productivity. The frequency density formula can assist you in providing those needs.
|
Delay (days) |
Frequency |
Width (days) |
Frequency Density |
|
0-5 |
4 |
6 |
0.67 |
|
6-10 |
8 |
5 |
1.6 |
|
11-15 |
10 |
5 |
2.0 |
|
16-30 |
12 |
15 |
0.8 |
For instance, the table above explains the concentrated delay in construction planning. It shows that the 16-30 group has the most frequency with 12 days. However, it has a width of 15, so the result is spread out, making it less critical per unit. The real issue is in the 11-15 days group because it has a frequency density of 2.0, the most than others.
The help of the frequency density formula for constructing a building
In the construction industry, the frequency density formula has a crucial role. It is a useful tool to interpret and analyse grouped data. In particular, when there are intervals that cause inequality between the group. This method is valuable in some areas, such as soil testing, where engineers often look for moisture content, compaction, and density at a few depths.
When measuring the soil, there are going to be layers that have wider intervals. If you use regular frequency counts, the result you will get will be misleading. With the frequency density formula, you can compare the data fairly based on certain values within different ranges. As a result, this will help engineers and construction planners to have an accurate understanding of soil behaviour.
However, this is not the only usage of the frequency density formula. It offers many uses to contribute to constructing a building, like revealing potential weaknesses or critical points to ensure safety standards. Furthermore, it allows you to improve productivity bottlenecks through smarter planning and resource management. Other than this method, there are many ways to improve the building safety. The College of Contract Management has amazing courses that are ready to help you improve your method in construction. Grab the courses and receive the benefits!
