Inequality Worksheets

Let us look at a simple example to understand frequency distribution. We will consider the marks that 10 students from a class have obtained in a science test. The marks are our raw data, and they are as follows:

32, 26, 12, 37, 24, 07, 31, 40, 22, 29.

After this, we will consider the statistical measure that we refer to as range. It is the difference that we get between the data set’s largest value and the smallest value. So, looking at the data above, we get the range as

40-07= 33

Now, you see how tough the process will get if there is a larger number. If one has to include the test marks of all 40 students in the class, it will be a complex process to understand and analyze all the data if it is not organized.

Therefore, statistical interpretation’s objective is to organize data into an accessible form to make it easier for us to understand and analyze it.

What is Frequency Distribution

It is a graphical or tabular way of representing organized data using a measurement scale. Using a frequency distribution, you can make out the intensity or concentration points of data, analyze the highs and lows, and derive firm conclusions for decision-making. If you need to observe the distribution of individual observations, using frequency distribution is the right way to go about it.

Common Terminologies

• Class Frequency: A class frequency meaning is a measure of the number of values present in one class. For example, if 5 students belong to the height range of 155 cm to 160 cm in a classroom, the class frequency for the 155-160 cm range is 5. 

• Class Limits: The upper and lower limits of a class are called the upper-class limit and the lower-class limit, respectively. 

• Class Width: The answer obtained after subtracting the lower-class limit from the upper-class limit is called the class width. 

• Class Mark or Class Midpoint: It is the sum of the upper and lower-class limits divided by 2. The middle value of a class represents the entire class. 

• Frequency Curve: The graphical representation of a frequency distribution on the X-axis and Y-axis is called a frequency curve. 

Use of a Frequency Distribution Graph

It offers us a way of organizing data to make it more meaningful. That’s where preparing a 

frequency distribution graph is required. A frequency distribution chart will summarise all the data under 2 columns. They are variables/categories followed by their frequency. The first column will list all the results as individual values or in the coupled value; it all depends on the data set’s size. The second column is about the tally marks of each result. Also, this column is optional. Finally, the third column lists down the frequency of each outcome. You must have noticed that in our daily lives, we see a lot of information that is present in the form of numerical figures, graphs, tables, and more.

Data refers to the collection of bits of information, measurements, or observations. And raw data is the initial collection of information. This information is still not organized. At the first step of collecting information, you will get raw data. For example, if you go around and ask any random five people their favorite colors, they provide you with the answers blue, green, yellow, red, white; this is raw data. 

Then there are two types of data, i.e., discrete and continuous data. Discrete data is listed in whole numbers, like the number of children in a school or animals in a zoo. It cannot be in decimals or fractions. Continuous data is not in whole numbers; it can be in decimals. Examples are the temperature in a city for a month or your percentage of marks for the last exam, etc.

Applications of Frequency Distribution Table:

There are two kinds of frequency distribution tables. One is an ungrouped frequency distribution table, and the other is a grouped frequency distribution table. Further, let’s take a look at some of the observations that have been derived from the frequency distribution table method:

• In the table that we use to measure the data frequency, we can easily observe the number of times the data appears in the data that use frequency.
• The table assists in measuring the distribution, such as variance, range, and standard variation.
• The range refers to the variation between higher and lower values of the data provided.
• After that, the mean, median, and mode get measured.
• The table then assists in deciding the symmetry or asymmetry’s length.

Conclusion:

We learned that the frequency distribution table in statistics allows finding the data in a simple tabular form. Moreover, it becomes easy to understand. Frequency and tally marks are the fundamental features needed to construct a frequency distribution table. Also, representing data by using a Frequency Distribution Formula table is very easy. The frequency distribution table’s applications and properties assist us in straightforwardly exploring the data features.