Direction: A table is given below, study the table carefully and answer the following question. The given table represents the marks obtained by four students W. X, Y and Z in four subjects P, C, B and M. with the maximum marks in each subject being 100. Stu/sub P C B M W 70 90 50 85 X 55 80 95 60 Y 60 20 90 40 Z 90 80 40 65 The difference between the highest and the lowest percentage (P, C, M and B together) among the four students is:
21.25
Understanding the Student Marks Data and Percentage Calculation
The question asks us to find the difference between the highest and lowest percentages obtained by four students (W, X, Y, and Z) across four subjects (P, C, B, and M). The maximum marks for each subject are 100. To solve this, we first need to calculate the total marks obtained by each student and then convert these total marks into a percentage.
Let's look at the provided table showing the marks:
| Stu/Sub | P | C | B | M |
|---|---|---|---|---|
| W | 70 | 90 | 50 | 85 |
| X | 55 | 80 | 95 | 60 |
| Y | 60 | 20 | 90 | 40 |
| Z | 90 | 80 | 40 | 65 |
Calculating Total Marks for Each Student
The total marks for each student are the sum of their marks in subjects P, C, B, and M.
- Student W: \(70 + 90 + 50 + 85 = 295\)
- Student X: \(55 + 80 + 95 + 60 = 290\)
- Student Y: \(60 + 20 + 90 + 40 = 210\)
- Student Z: \(90 + 80 + 40 + 65 = 275\)
The total maximum marks for all four subjects combined is \(100 + 100 + 100 + 100 = 400\).
Calculating Percentage for Each Student
The percentage for each student is calculated using the formula:
\(\text{Percentage} = \left(\frac{\text{Total Marks Obtained}}{\text{Total Maximum Marks}}\right) \times 100\)
Let's calculate the percentage for each student:
- Student W: \(\left(\frac{295}{400}\right) \times 100 = \left(\frac{295}{4}\right)\% = 73.75\%\)
- Student X: \(\left(\frac{290}{400}\right) \times 100 = \left(\frac{290}{4}\right)\% = 72.50\%\)
- Student Y: \(\left(\frac{210}{400}\right) \times 100 = \left(\frac{210}{4}\right)\% = 52.50\%\)
- Student Z: \(\left(\frac{275}{400}\right) \times 100 = \left(\frac{275}{4}\right)\% = 68.75\%\)
Here is a summary of the percentages:
| Student | Total Marks | Percentage |
|---|---|---|
| W | 295 | 73.75% |
| X | 290 | 72.50% |
| Y | 210 | 52.50% |
| Z | 275 | 68.75% |
Finding the Difference Between Highest and Lowest Percentage
Now we need to identify the highest and lowest percentages among the four students.
- Highest Percentage: 73.75% (Student W)
- Lowest Percentage: 52.50% (Student Y)
The difference between the highest and the lowest percentage is:
\(\text{Difference} = \text{Highest Percentage} - \text{Lowest Percentage}\)
\(\text{Difference} = 73.75\% - 52.50\%\)
\(\text{Difference} = 21.25\%\)
The difference between the highest and the lowest percentage among the four students is 21.25.
Revision Table: Key Calculations
| Student | Total Marks | Percentage |
|---|---|---|
| W | 295 | 73.75% |
| X | 290 | 72.50% |
| Y | 210 | 52.50% |
| Z | 275 | 68.75% |
Highest Percentage = 73.75%
Lowest Percentage = 52.50%
Difference = \(73.75 - 52.50 = 21.25\)
Additional Information on Percentage Concepts
Understanding percentages is crucial in data interpretation questions like this. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign ("%") or the abbreviation "pct.". In this problem, we calculated the overall percentage obtained by each student by comparing their total score to the maximum possible total score.
When dealing with multiple subjects with potentially different maximum marks, the method would be slightly different. You would sum up the maximum marks for all subjects to get the total maximum marks and sum up the student's marks in all subjects to get the total obtained marks. The percentage calculation remains the same: (Total Obtained Marks / Total Maximum Marks) * 100.
Finding the difference between the highest and lowest values in a dataset is a common task in data analysis to understand the range or spread of the data points.
Similar Questions
What is the average marks of the four students in P?
Direction: The following table gives the details of the number of students in Class 10, Section A and B, who had taken the midterm and final exams.
Result
Section A
Section B
Total number of students who failed in both the exams
28
23
Number of students who failed in the
midterm but passed in the final exam
14
12
Number of students who passed in the
midterm but failed in the final exam
6
17
Number of students who passed in both the exams
64
55
Based on the given data, the percentage of Section A students who passed the annual exam is_____.
- The given table represents the marks obtained by four students W, X, Y and Z in four subjects P, C, B and M with the maximum in each subject being 100
Stu/sub
P
C
B
M
W
70
90
50
85
X
55
80
95
60
Y
60
20
90
40
Z
90
80
40
65
Based on the given data. Find W's marks percentage in P, C and B combined together. Based on the given table, the percentage salary increase during the period 2001-2006 was (round off to the nearest integer).
Direction: The given table represents the marks obtained by four students W, X, Y and Z in four subjects P, C, B and M , the maximum marks in each subject being 100.
Stu/sub
P
C
B
M
W
70
90
50
85
X
55
80
95
60
Y
60
20
90
40
Z
90
80
40
65
Based on the given data, the student who got the lowest percentage in P, C, M, and B combined is:
Direction: The given table represents the marks obtained by four students W, X, Y and Z in four subjects P, C, B and M and the maximum marks in each subject being 100.
Stu/sub
P
C
B
M
W
70
90
50
85
X
55
80
95
60
Y
60
20
90
40
Z
90
80
40
65
The average marks of the four students in M is:
The following table shows the gain in weight by 25 children in a year. What is the mean value of gain in weight?
Gain in weight (in kg) No. of children 1.5 4 2 5 2.4 8 3 5 3.2 2 3.4 1 The total percentage of illiterates in all the four cities is _______ (round to one decimal place).
City
Population
Literate
illiterate
% of literate
A
200
150
50
-
B
-
200
100
66.6
C
150
50
100
-
D
120
-
90
25
Important Questions from Tabulation
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In which state, the number of patients who recovered from covid-19 steadily decreasing?
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Find the difference between the total number of patients recovered from Covid-19 in all months in Punjab and the total number of patients recovered from Covid-19 in all months in Rajasthan.
In February 2021 the number of patients recovered from Covid-19 in Punjab is how much approximant percent more/less than the number of patients recovered from Covid-19 Uttar Pradesh in the same month?
