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Frequency Distribution Table Statistics

 

In statistics, data is the fundamental unit of all operations. In simple words, data is a piece of information or fact that can be used for analysis. A group of related information forms a collection of data. Weather forecast reports, marks in your progress card, the calendar, etc., are all examples of a collection of data. Statistics is a helpful tool, especially while working with large amounts of information. With the help of the information collected, statistics can predict the nature and trends of future data. The real-world applications of this tool range from estimating the population of a country in the next decade to forecasting the weather tomorrow. The data collected can be represented in many forms like charts, graphs, or tables. A frequency distribution table illustrates the occurrence of various data in an observation.

Problem 1

What is the frequency of the number 5 in the list of numbers?

(1,1,1,2,2,3,5,5,5,5,6,7,7,7,7,8,9,)

Solution 1

Since the number 5 occurs four times, the frequency of 5 is 4.

Problem 2

Tabulate the frequency distribution of marks of 30 students who scored 90 and above in an exam.

The marks of the students are given below.

(100,98,96,91,93,97,94,98,90,93,94,100,94,92,97,94,96,98,94,94,97,90,95,93,96,98,96,91,93,95)

Solution 2

Marks Number of students(frequency)
90 2
91 2
92 1
93 4
94 6
95 2
96 4
97 3
98 4
99 0
100 2
Total 30

We know that frequency is the occurrence of a particular data. To solve this problem, we have to count the number of students who obtained a certain mark. Only two students score 90, and hence the frequency is 2. Similarly, we did the same for all the marks till 100. To check if we have considered all the data, count the total frequency that adds up to 30.

The above table represents an ungrouped frequency table. We can work with this type of table when the amount of data is limited. When there is a large amount of data, it is easier to use a grouped frequency data. Here, data is subdivided into groups. Each group is called a class and every class has the same size in a frequency table.

An example of a grouped frequency distribution is shown below.

The table represents the average score of 70 batsmen in three matches.

Score Number of batsmen(frequency)
0-10 1
10-20 3
20-30 2
30-40 3
40-50 7
50-60 9
60-70 9
70-80 12
80-90 10
90-100 9
100-110 6
Total 70

Instead of finding the frequency of each score from 0 to 110, we divided the data into 11 groups or classes. Each class has a different lower and higher limit, but the class size is constant at 10.

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