Question

Srikanth is a class IX Mathematics teacher in Chennai. After a class test, he asks a student to record the marks that all the students obtained. Narayanan scored the least marks 6 in the class and Keerthana scored the highest marks 59 in the class out of 60 marks. He prepares a frequency distribution table using the collected data and draws a histogram as shown below:

1. What is the width of each class?
2. What is the total number of students in class IX?
3. How many students scored 50% and above marks?
4. What is the range of the collected data?

Answer 1

Histogram data representing student marks with class intervals (0-10, 10-20, 20-30, 30-40, 40-50, 50-60) and respective frequencies (2, 10, 21, 17, 9, 1), with the lowest mark being 6 and the highest being 59.

1. Width of each class:
   
   Width = Upper Limit − Lower Limit = 10 − 0 = 10  [Subtracting the lower limit from the upper limit of the first interval]
2. Total number of students:
   
   Total Students = 2 + 10 + 21 + 17 + 9 + 1 = 60  [Summing the frequencies of all class intervals]
3. Students scoring 50% and above marks:
   
   Passing Mark (50% of 60) = 30  [Calculating half of the maximum possible test marks]
   

   Total Students = 17 + 9 + 1 = 27  [Adding frequencies of classes 30-40, 40-50, and 50-60]
4. Range of the collected data:
   
   Range = Highest Value − Lowest Value = 59 − 6 = 53  [Subtracting the lowest score from the highest score]