Construct a grouped frequency distribution table for the following data giving the marks obtained by 45 students in a class test.
Start with a class interval of 0-5. Leftrightarrow26,30,12,10,20,20,6,23,19,9,14,13,5,17 10,11,25,5,11,7,24,6,21,9,6,10,9,27,4,30,12, 10, 20, 20, 6, 23, 13, 28, 17, 10, 24, 4, 21, 9
Answer the following questions based on the table.
a What is the upper class limit and the lower class limit of the class interval, 0-5?
b. How many students secured less than 10 marks?
c. If the maximum marks in the test were 30, how many students obtained 50% or more marks?
d. What percentage of students obtained less than 50% marks?
Answers
Step-by-step explanation:
Solution:
The lowest value in the data is 4 and the highest value is 30.
Taking the first class interval as 0-5 and the class size =5-0=5 .
We will have the following class intervals:
0 - 5, 5 - 10 - 15, 15 - 20 , 20-25, and 25-30.
Do we stop at 25-30?
No, because we have a value 30 in the given data, and we need a class interval that will include 30.
Thus, we will have one more interval 30-35.
Let us represent the data in the form of a grouped frequency distribution table.
( see the attachment )
a) For the class interval 0-5, the upper class limit is 5 and the lower class limit is 0.
b) To find the number of students who secured less than 10 marks, we will consider the total frequency of the class intervals 0-5 and 5-10 taken together.
As these two intervals do not include the observation 10.
Thus, 2 + 11 = 13 students secured less than 10 marks.
c) Let us find the 50% of 30.
50/100 × 30 = 15marks
Now, identify the intervals that include 15 marks and above: 15 - 20, 20 25, 25 25 - 30 , and 30- 35
Total number of students who obtained 50% or more marks = sum of the frequencies of the above four intervals =4+10+4+2=20
Thus, 20 students obtained 50% or more marks.
d) Total number of students
= Number of ervations = 45
Number of students obtaining less than 50% marks =45-20=25
Final answer = 55 5/9 %
