In a class of 8 students, the test scores are 10, 20, 15, 25, 30, 15, 25, 36 out of 50 in Geography subject. What is the average score of the class?
Answers
Answer:
To understand frequency distribution, let us first start with a simple example. We consider the marks obtained by ten students from a class in a test to be given as follows:
23, 26, 11, 18, 09, 21, 23, 30, 22, 11
This form of data is known as raw data. A statistical measure called range can be defined. It is the difference between the largest and smallest values of a data set. Here, range = 30 – 09 = 21.
Frequency Distribution Table
Now, imagine how difficult and cumbersome this process would get if there were a larger number of observations. If we were to include the test scores of all 20 students in this class, it would be very difficult to understand and interpret such data unless it is ‘organized’.
The objective of statistical interpretation is to organize data into a concise form so that interpretation and analysis become easy. It is for this reason that we organize larger data into a table called the frequency distribution table.
Ungrouped Data
Let the test scores of all 20 students be as follows:
23, 26, 11, 18, 09, 21, 23, 30, 22, 11, 21, 20, 11, 13, 23, 11, 29, 25, 26, 26
Note that the term frequency refers to the number of times an observation occurs or appears in a data set. Hence, in case of repetitions, the frequency increases. The table below will help you understand this better:
Marks obtained in the test No. of students (Frequency)
09 1
11 4
13 1
18 1
20 1
21 2
22 1
23 3
25 1
26 3
29 1
30 1
Total 20
In the example above, the frequency refers to the number of students getting a particular mark in the test. Also, note that your frequency must always total the number of observations after tallying. Here, the total we have obtained after tallying the test scores of the students is 20 which is also the number of observations given.
Read more about Bar Graphs and Histograms here in detail.
A frequency distribution such as the one above is called an ungrouped frequency distribution table. It takes into account ungrouped data and calculates the frequency for each observation singularly.
Grouped Data
Now consider the situation where we want to collect data on the test scores of five such classes i.e. of 100 students. It becomes difficult to tally for each and every score of all 100 students. Besides, the table we will obtain will be very large in length and not understandable at once. In this case, we use what is called a grouped frequency distribution table.
Learn more about Range and Mean for Grouped Data here in