Mathematics
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 :
(i) What is the width of each class ?
(ii) What is the total number of students in class IX ?
(iii) How many students scored 50% and above marks ?
(iv) What is the range of the collected data ?
Statistics
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Answer
| Marks | Number of students |
|---|---|
| 0 - 10 | 2 |
| 10 - 20 | 10 |
| 20 - 30 | 21 |
| 30 - 40 | 17 |
| 40 - 50 | 9 |
| 50 - 60 | 1 |
(i) Class width = Upper limit of a class - Lower limit of a class
= 10 - 0 = 10.
Hence, width of each class = 10.
(ii) Total number of students = 2 + 10 + 21 + 17 + 9 + 1 = 60.
Hence, total number of students = 60.
(iii) 50% of 60 marks = 30 marks
∴ Number of students who scores 50% and above marks are:
30 - 40 ⟶ 17 students
40 - 50 ⟶ 9 students
50 - 60 ⟶ 1 student
∴ Total students = 17 + 9 + 1 = 27.
Hence, students scoring 50% and above marks = 27.
(iv) Range = Highest mark - Lowest mark
= 59 - 6
= 53.
Hence, range of the data = 53.
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