The following table shows the marks of 90 students in a test of 80 marks: Marks Number of Students 1 – 10 5 11 – 20 8 21 – 30 10 31 – 40 13 41 – 50 18 51 – 60 17 61 – 70 12 71 – 80 7
The percentage of students who have obtained less than or equal to 50% marks is
40%
Calculating Percentage of Students from Marks Distribution Table
This question asks us to find the percentage of students who scored less than or equal to 50% marks in a test that was conducted for a total of 80 marks. To solve this, we first need to determine the mark value that corresponds to 50% of the total marks and then use the provided frequency distribution table to count the number of students who scored at or below this mark value.
Step 1: Determine the Mark Value for 50%
The total marks for the test are 80. To find 50% of 80 marks, we perform the following calculation:
\(50\% \text{ of } 80 = \frac{50}{100} \times 80\)
\(= 0.50 \times 80\)
\(= 40\)
So, students who obtained less than or equal to 50% marks are those who scored 40 marks or less.
Step 2: Identify Students Scoring Less Than or Equal to 40 Marks Using the Table
The provided table shows the number of students in different mark ranges (class intervals). We need to find the number of students in the intervals where the upper limit is less than or equal to 40. Let's look at the table:
| Marks | Number of Students |
| 1 – 10 | 5 |
| 11 – 20 | 8 |
| 21 – 30 | 10 |
| 31 – 40 | 13 |
| 41 – 50 | 18 |
| 51 – 60 | 17 |
| 61 – 70 | 12 |
| 71 – 80 | 7 |
We are interested in students who scored less than or equal to 40 marks. This includes students in the following mark intervals:
- 1 – 10 marks: 5 students
- 11 – 20 marks: 8 students
- 21 – 30 marks: 10 students
- 31 – 40 marks: 13 students
Step 3: Calculate the Total Number of Students Scoring Less Than or Equal to 40 Marks
To find the total number of students who scored 40 marks or less, we sum the number of students in the intervals identified in Step 2:
Total students with marks \(\le 40 = 5 + 8 + 10 + 13\)
\(= 36\) students
Step 4: Calculate the Percentage of Students
The total number of students who took the test is given as 90 (also confirmed by summing the 'Number of Students' column: \(5+8+10+13+18+17+12+7 = 90\)).
The percentage of students who obtained less than or equal to 50% marks (i.e., \(\le 40\) marks) is calculated as:
Percentage \( = \left( \frac{\text{Number of students with marks } \le 40}{\text{Total number of students}} \right) \times 100\)
Percentage \( = \left( \frac{36}{90} \right) \times 100\)
Percentage \( = \left( \frac{36 \div 18}{90 \div 18} \right) \times 100\)
Percentage \( = \left( \frac{2}{5} \right) \times 100\)
Percentage \( = 0.4 \times 100\)
Percentage \( = 40\%\)
Therefore, the percentage of students who have obtained less than or equal to 50% marks is 40%.
Revision Table: Key Concepts in Student Marks Analysis
| Concept | Description | How it Applies Here |
| Total Marks | Maximum possible score in a test. | Used to determine the threshold for 50% marks (80 marks). |
| Percentage Marks | Score expressed as a fraction of total marks, multiplied by 100. | We calculated 50% of total marks to set the scoring threshold. |
| Frequency Distribution Table | A table showing how often each value or range of values occurs in a dataset. | Used to find the number of students within specific mark ranges. |
| Class Interval | A range of values within a frequency distribution table. | The table uses intervals like 1-10, 11-20, etc. |
| Cumulative Frequency | The total frequency up to the upper limit of a class interval (sum of frequencies up to that class). | Implicitly used by summing frequencies of intervals below the threshold. |
Additional Information: Analyzing Grouped Student Data
When student marks are presented in grouped frequency tables like the one in the question, we are dealing with grouped data. We don't know the exact score of each student, only which range their score falls into. However, for questions involving thresholds like "less than or equal to a certain mark", we can sum the frequencies of all class intervals whose upper limit is below or at the specified threshold. This allows us to determine the number of students meeting that criteria.
Understanding cumulative frequency is also helpful here. The cumulative frequency for the 31-40 interval is the total number of students scoring up to 40 marks. This is the sum of frequencies for 1-10, 11-20, 21-30, and 31-40 intervals.
Calculating percentages from grouped data involves finding the number of items (students) in the relevant groups and dividing by the total number of items, then multiplying by 100. This is a fundamental skill in data analysis and statistics.
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Important Questions from Tabulation
Table shows income (in Rs.) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38000
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
By what percent are the Arrears of Amit and Suresh taken together less than the Arrears of Nitin and Varun taken together?The table given below shows the GDP of two countries in different five years.
Country Years A B Y1 175 285 Y2 200 300 Y3 150 125 Y4 75 85 Y5 50 95 K1 = The value of average GDP of country A in all the 5 years.
K2 = The value of average GDP of country B in all the 5 years.
What is the value of (K1 + K2)?
Study the Table Properly and answer by interpreting the data
The table shows the percentage population of five districts in a state below poverty line and the proportion of males and females.
District Percentage of population
below poverty levelProportion of Male and Female Below poverty line (M:F) Above poverty Line (M:F) D1 15 2 : 3 3 : 2 D2 18 3 : 4 7 : 5 D3 20 2 : 5 3 : 4 D4 25 5 : 2 4 : 3 D5 12 3 : 7 2 : 7 If the total population in the district D3 is 40,000, then what is the population of below poverty line in the district D3, ?
The table given below shows the marks obtained by 4 students in 5 subjects. The maximum marks of each subject is 100.
Subjects
Students
P1
P2
P3
P4
S1
89
100
92
91
S2
62
52
72
37
S3
57
55
70
65
S4
76
85
76
58
S5
85
70
66
62
What is the total percent marks of P4?
The data given below shows the number of people who have saved a certain amount of money.
Savings
(in Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the mode of the given data?
