Science Laws

how to calculate Aggregate CGPA of different semesters

Calculating your CGPA is an essential skill to track your academic performance, whether you are calculating it for 4 semesters, 6 semesters, 8 semesters, or the entire duration of your course. By understanding the simple steps of multiplying grade points with credit hours, summing them up, and dividing by the total credit hours, you can easily determine your CGPA for any number of semesters.

Always remember that CGPA is just one measure of academic success, but it should be combined with your skills, passion, and other qualities that make you stand out.

How to Calculate Aggregate CGPA of Different Semesters?

In the world of academia, CGPA (Cumulative Grade Point Average) is one of the most crucial metrics for evaluating a student's performance. Whether you are a high school student or a university graduate, understanding how to calculate your CGPA is important for tracking your academic progress.

This article will guide you through the process of calculating the aggregate CGPA of different semesters, with a specific focus on how to calculate the aggregate CGPA of 4, 6, and 8 semesters, and your overall CGPA.

What is CGPA?

CGPA stands for Cumulative Grade Point Average, which is the average of your grade points across multiple semesters or years. It helps to provide a more comprehensive understanding of your academic performance by considering all the grades you have earned over time. CGPA is widely used in colleges and universities to give an overall score for students.

Understanding the Formula for CGPA

The CGPA calculation typically follows a standardized formula, but it can vary depending on the institution or university. Generally, CGPA is calculated by the following formula:

CGPA = (Total Grade Points Earned) / (Total Credit Hours)

Grade Points Earned: The grade you received in each subject is converted into grade points.
Credit Hours: Every subject or course has a certain number of credit hours assigned based on its importance or duration.

How CGPA is Awarded?

In most universities, grade points are assigned according to the letter grades. Below is a general representation of how grades are converted into grade points:

Letter Grade	Grade Points (Scale 10)
O (Outstanding)	10
A+ (Excellent)	9
A (Very Good)	8
B+ (Good)	7
B (Above Average)	6
C+ (Average)	5
C (Below Average)	4
D (Pass)	3
F (Fail)	0

How to Calculate Aggregate CGPA for Different Semesters?

When you are calculating the aggregate CGPA, it is essential to include the grade points from each semester and the credit hours associated with those courses. Below, we will explain how to calculate the aggregate CGPA for 4, 6, 8 semesters, and your overall CGPA.

1. How to Calculate Aggregate CGPA of 4 Semesters?

To calculate the aggregate CGPA of 4 semesters, follow these steps:

Find the Grade Points for Each Course: For each course in all 4 semesters, identify the grade points based on the grades you received.
Determine Credit Hours for Each Course: Identify the credit hours assigned to each course.
Calculate Total Grade Points: Multiply the grade points by the credit hours for each course and add them up.
Calculate Total Credit Hours: Add up the total credit hours for all the courses over the 4 semesters.
Apply the Formula: Finally, divide the total grade points by the total credit hours to get your aggregate CGPA.

Example: If you have the following data for 4 semesters:

Semester	Course	Grade Points	Credit Hours
1	Math	8	4
1	Science	9	3
2	History	7	4
2	English	8	3
3	Physics	9	4
3	Biology	8	3
4	Chemistry	7	4
4	Computer Science	9	3

Calculate the total grade points:
(8×4) + (9×3) + (7×4) + (8×3) + (9×4) + (8×3) + (7×4) + (9×3) = 32 + 27 + 28 + 24 + 36 + 24 + 28 + 27 = 226
Calculate the total credit hours:
4 + 3 + 4 + 3 + 4 + 3 + 4 + 3 = 28
Calculate CGPA:
CGPA = 226 / 28 = 8.07

Thus, your aggregate CGPA for these 4 semesters is 8.07.

2. How to Calculate Aggregate CGPA of 6 Semesters?

The method to calculate the aggregate CGPA for 6 semesters is similar to the one for 4 semesters. You will need to:

Collect the grade points and credit hours for all 6 semesters.
Multiply the grade points by the respective credit hours for each course.
Add the total grade points and total credit hours.
Divide the total grade points by the total credit hours.

Example: Let's say the data for 6 semesters is as follows:

Semester	Course	Grade Points	Credit Hours
1	Math	8	4
1	Science	9	3
2	History	7	4
2	English	8	3
3	Physics	9	4
3	Biology	8	3
4	Chemistry	7	4
4	Computer Science	9	3
5	Geography	8	4
5	Economics	7	3
6	Philosophy	9	4
6	Psychology	8	3

Calculate the total grade points:
(8×4) + (9×3) + (7×4) + (8×3) + (9×4) + (8×3) + (7×4) + (9×3) + (8×4) + (7×3) + (9×4) + (8×3) = 32 + 27 + 28 + 24 + 36 + 24 + 28 + 27 + 32 + 21 + 36 + 24 = 359
Calculate the total credit hours:
4 + 3 + 4 + 3 + 4 + 3 + 4 + 3 + 4 + 3 + 4 + 3 = 40
Calculate CGPA:
CGPA = 359 / 40 = 8.98

Thus, the aggregate CGPA for these 6 semesters is 8.98.

3. How to Calculate Aggregate CGPA of 8 Semesters?

To calculate the CGPA for 8 semesters, the steps are exactly the same as for the previous two cases.

You would gather the grade points and credit hours for each semester, calculate the total grade points and total credit hours, and then divide them to get the CGPA.

4. How to Calculate Overall CGPA?

The overall CGPA is the cumulative grade point average that spans the entire duration of your degree program. It includes the grade points from all the semesters you have completed so far.

To calculate your overall CGPA:

Gather the data for all semesters: Collect your grade points and credit hours for all semesters, whether it’s 4, 6, 8, or more semesters.
Follow the same procedure as above: Multiply the grade points for each course by the corresponding credit hours, then sum them up.
Apply the CGPA formula: Divide the total grade points by the total credit hours to get your overall CGPA.

How do I combine my CGPA of all semesters?

To combine your CGPA from all semesters, you essentially need to calculate the aggregate CGPA, which takes into account the grade points and credit hours from each semester. The process involves the following steps:

Steps to Combine Your CGPA from All Semesters:

List Grade Points and Credit Hours for Each Semester:
- For each course in every semester, note the grade points (on the 10-point scale) and the credit hours.
Multiply Grade Points by Credit Hours:
- For each course, multiply the grade points by the corresponding credit hours. This gives you the weighted grade points for each course.
Example:
If you received 8 grade points in a course worth 3 credit hours:
Weighted Grade Points = 8 × 3 = 24
Calculate Total Grade Points for Each Semester:
- Add up the weighted grade points for all courses within a semester to get the total grade points for that semester.
Calculate Total Credit Hours for Each Semester:
- Add up the credit hours for all courses in the semester to get the total credit hours for that semester.
Calculate the CGPA for Each Semester:
- Use the formula: $\text{CGPA for the Semester} = \frac{\text{Total Grade Points for the Semester}}{\text{Total Credit Hours for the Semester}}$
This will give you the CGPA for each individual semester.
Calculate Aggregate CGPA:
- To combine your CGPA across multiple semesters, follow these steps:
  1. Sum the total weighted grade points for all semesters.
  2. Sum the total credit hours for all semesters.
  3. Divide the total weighted grade points by the total credit hours.
Formula for Aggregate CGPA:
$\text{Aggregate CGPA} = \frac{\text{Total Weighted Grade Points from all Semesters}}{\text{Total Credit Hours from all Semesters}}$

Example of Combining CGPA from 3 Semesters

Let’s say you have completed 3 semesters with the following data:

Semester 1:

Course 1: Grade Points = 8, Credit Hours = 3
Course 2: Grade Points = 7, Credit Hours = 4
Total Grade Points = (8×3) + (7×4) = 24 + 28 = 52
Total Credit Hours = 3 + 4 = 7
CGPA for Semester 1 = 52 / 7 = 7.43

Semester 2:

Course 1: Grade Points = 9, Credit Hours = 3
Course 2: Grade Points = 8, Credit Hours = 4
Total Grade Points = (9×3) + (8×4) = 27 + 32 = 59
Total Credit Hours = 3 + 4 = 7
CGPA for Semester 2 = 59 / 7 = 8.43

Semester 3:

Course 1: Grade Points = 7, Credit Hours = 3
Course 2: Grade Points = 8, Credit Hours = 4
Total Grade Points = (7×3) + (8×4) = 21 + 32 = 53
Total Credit Hours = 3 + 4 = 7
CGPA for Semester 3 = 53 / 7 = 7.57

Calculating Aggregate CGPA:

Total Grade Points (from all semesters):
- Semester 1: 52
- Semester 2: 59
- Semester 3: 53
- Total Grade Points = 52 + 59 + 53 = 164
Total Credit Hours (from all semesters):
- Semester 1: 7
- Semester 2: 7
- Semester 3: 7
- Total Credit Hours = 7 + 7 + 7 = 21
Aggregate CGPA:
$\text{Aggregate CGPA} = \frac{164}{21} = 7.81$

So, the aggregate CGPA across these 3 semesters is 7.81.

Key Points to Remember:

You need to consider the credit hours of each course because courses with more credit hours weigh more in the CGPA calculation.
The aggregate CGPA reflects your overall performance, so it's a cumulative score that combines the results from all your semesters.
If you have a large number of semesters, follow the same approach, and ensure all grade points and credit hours are added correctly.

This method will help you combine your CGPA across any number of semesters (4, 6, 8, etc.).

Aditya Raj Anand

How to write an application for demand draft of education loan

letter

How to Write an application for demanding draft of educational loan. This application is written when someone has applied for educational loan. And they wants some money from Bank. For examples it may be for tuition fees, hostel fees, etc.

Following are the Format and steps of writing a draft demand education loan application.

1. To,

2. The Accounts Department Head of Bank

3. [Bank Name]

4. [Your college Name]

6. [Your college address]

7. Sub:- Demand draft of education loan.

Respected Sir,

I am [Your Name]. son of/Daughter of [Your Father or Mother name]. My age is [date o birth]. I am currently studying at [college name]. Branch [Branch name] seek to avail the loan demand letter on dated [Date] for Processing of educational loan Form:

[Bank Name______________________]

[Bank Address______________________]

[Branch Name_______________________]

For following fees:

Tuition Fees
Bus Fees
Room rent fees
Coaching fees
College Fees
Exam fees

I Therefore, requested you to please grant me loan amount of all the subtotal fees regarding my University [college Name] Policy guidelines.

Your Sincerely

[Name]

[Address]

[Signature]

How to write an application for demand draft of education loan

These are following 5 sample format of writing an application for demand draft of education loan. This letter is written to the Bank manager as well as to the Registrar account department head. The following different - different format makes you understand in best clarity way.

#1 writing a demand draft of education loan

1. To,

2. The Registrar of Bank head

3. [Bank Address]

4. [Bank Name]

5. [Branch Name]

6. [College Name and Address]

7. Subject:

#2 writing a letter to bank manager for demand draft

1. To,

2. Bank Manager

3. [Bank Name]

4. Branch Name]

5. Bank address]

6. [Your college Name]

7. Subject

8. Body

9. Your Signature

#3 writing a letter to bank manager for education loan

1. To,

2. The Bank Manager

3. [Bank Name]

4. [Bank Address]

5. Subject: Issue for education loan

Respected Sir,

Most Humbly and respectfully I want to say that I am your old bank customer of [Bank Name]. Branch [Branch Name] located at [Bank address]. I have a saving/current account in your bank. I am also studying in [College/University Name with class]. I am troubling to pay the my college/University fees. So I need some money. Can I get some student education loan from your Bank.

I, Therefore, requested you to please reply me soon as possible. I there is any loan policy criteria then please suggest me to do that. Regards education loan policy owned by Government of India.

Your Sincerely

[Name]

[Account No.]

[Signature]

Now, let's see some more sample for demand letter format for education loan. If you are also searching for demand letter for college fees, or may be demat Letter for demand letter for education loan from college then you are on the right place. Science laws will give you full knowledge.

Below is a sample format for a demand letter for an education loan:

[Your Name]
[Your Address]
[City, State, Pin Code]
[Phone Number]
[Email Address]

[Date]

[College name who give you loan or Loan Institution Name]
[Address of Lender/Institution]
[City, State, Pin Code]

Subject: Demand for repayment for education loan.

Dear Sir/Madam,

I hope this letter finds you well. I am writing to formally request the repayment of the education loan I obtained from your institution, which was sanctioned under the terms and conditions agreed upon at the time of the loan approval.

Below are the details of the loan:

Loan Account Number: [Insert Account Number]
Date of Loan Sanction: [Insert Date]
Loan Amount: [Insert Loan Amount]
Total Outstanding Amount: [Insert Outstanding Amount]
Due Date for Repayment: [Insert Due Date]
EMI Amount: [Insert EMI Amount]

As per the loan agreement, the repayment of the loan was to commence from [insert date]. However, I regret to inform you that, despite repeated reminders and notices, I have not received any formal communication from your office regarding the status of my loan repayment or any further instructions.

Therefore, I am hereby requesting that the repayment of the outstanding loan amount be initiated at the earliest as per the terms outlined in the agreement. I would appreciate receiving the repayment schedule, along with any additional interest or charges that may apply due to the delay.

I understand the consequences of failing to honor the terms of the loan agreement and assure you of my commitment to settling the amount owed. Kindly consider this letter as a formal demand for repayment.

I request a prompt response and look forward to your assistance in resolving this matter without further delays. Should you require any additional documentation or information, please do not hesitate to contact me at [your contact number] or via email at [your email address].

Thank you for your immediate attention to this matter.

Sincerely,
[Your Full Name]
[Your Signature] (if submitting a hard copy)

You can adjust the details as per your specific case. Make sure to include the correct information about your loan, including amounts, dates, and any other relevant facts.

Aditya Raj Anand

Relationship of mean, median and mode | Derivation

math

The relationship between mean median and mode is the difference between mean and mode is almost equal to the three times of the difference between mean and median. It is also known as the empirical relation between mean median and mode. it is given by,

Mean − Mode = 3 (Mean − Median)

Empirical relation between mean median and mode

The difference between Mean and mode is equal to the three times the difference between mean and median. that is given by, Mean − Mode = 3 (Mean − Median).

As we understand that the empirical relation between mean median and mode is Mean − Mode = 3 (Mean − Median). but how to get relation to the reference of mean, median and mode. so here below are the relation between mean median and mode taken mean, median, mode as single term.

general relation between mean, median and mode is, Mean − Mode = 3 (Mean − Median).

take Mean as single term:-

Mean − Mode = 3 (Mean − Median)

Soln:-

= Mean − Mode = 3 Mean − 3 Median

= 3 Median − Mode = 3 Mean − Mean

= 3 Median − Mode = 2 Mean

= (3 Median − Mode)/2 = Mean

∴ Mean = (3/2 Median − 1/2 Mode

take Median as single term:-

Mean − Mode = 3 (Mean − Median)

soln:-

= Mean − Mode = 3 Mean − 3 Median

= 3 Median − Mode = 3 Mean − Mean

= 3 Median − Mode = 2 Mean

∴ Median = 2/3 Mean + 1/3 Mode

take mode as single term:-

Mean − Mode = 3 (Mean − Median)

Soln:-

= Mean − Mode = 3 Mean − 3 Median

= 3 Median − Mode = 3 Mean − Mean

= 3 Median − Mode = 2 Mean

∴ Mode = 3 Median − 2 Mean

Please note:-

that empirical relation between mean median and mode for normal distribution (or symmetrical distribution) is mean = median = mode. on the other hand the mean median and mode are equal to each other for normal distribution (or symmetrical distribution).

The empirical relation between mean median and mode for asymmetrical distribution is mean ≠ mode ≠ median. on the other hand the mean median and mode are not equal to each other for asymmetrical distribution.

Relation between mean median and mode

The relationship between the mean, median, and mode provides insights into the shape and distribution of data. Here's a breakdown of their relationship:

1. For Symmetric Distributions:

When a dataset is symmetric (i.e., it has a balanced distribution of values around a central point), the mean, median, and mode tend to be very close to each other.
Example: In a perfectly symmetric distribution (like a normal distribution), the mean, median, and mode will all be equal.

Illustration:
- Mean ≈ Median ≈ Mode

2. For Skewed Distributions:

Right (Positively) Skewed Distribution:

In a right-skewed distribution (where there are more values on the left side of the distribution and a few larger values on the right), the mean is typically greater than the median, and the median is greater than the mode.
Example: If most of the data points are small, but there are a few very large values, the mean is pulled in the direction of the larger values.

Illustration:
- Mode < Median < Mean
This suggests that the data has a "tail" on the right side.

Left (Negatively) Skewed Distribution:

In a left-skewed distribution (where there are more values on the right side and a few smaller values on the left), the mean is typically less than the median, and the median is less than the mode.
Example: If most of the data points are large, but there are a few very small values, the mean is pulled toward the smaller values.

Illustration:
- Mean < Median < Mode
This suggests that the data has a "tail" on the left side.

3. For Bimodal Distributions:

In a bimodal distribution (which has two modes), the mean can be influenced by the values of both peaks. The median will fall between the two modes, and the mode will refer to the two most frequent values.
In such cases, the relationship between the mean, median, and mode can vary greatly depending on the data.

Illustration (Example with two modes):

Mode 1 ≠ Mode 2, Median ≠ Mean.

Summary of the General Relationship:

Symmetric Distribution: Mean ≈ Median ≈ Mode
Right-Skewed Distribution: Mode < Median < Mean
Left-Skewed Distribution: Mean < Median < Mode

This relationship helps in identifying the skewness of the data, which is useful for data analysis and interpretation.

Derivation of relation between mean median and mode

Mean − Mode = 3 (Mean − Median)

= Mean − Mode = 3 Mean − 3 Median

= 3 Median = 3 Mean − Mean + Mode

= 3 Median = 2 Mean + Mode

= Median = 2/3 Mean + 1/3 Mode

Hence, the formula of relation between mean median and mode is Median = 2/3 Mean + 1/3 Mode.

Please note that you can also understand mean median and mode by the following examples.

mean median and mode examples

Suppose we want to compare the wage distribution of workers in two factories and determine which factory pays more to its workers. If we compare on the basis of individual workers, we cannot conclude anything. However, if for the given data, we get a representative value that signifies the characteristics of the data, the comparison become easy.

A certain value representative of the whole data and signifying its characteristics is called an average of the data.

Three types of averages are useful for analysing data. They are:-

Mean
Median
Mode

The relation between mean median and mode is a very famous relation and it is also called the empirical relation between mean median and mode as we know above. here is also a complete information about mean median and mode. we all are studying mean median and mode from class 10. but In class 10 we have a little bit idea that what is mean median and mode. here we will discuss about the actual meaning of mean median and mode. like what is mean? what is median? what is mode? in detail. so lets start with Mean.

What is mean?

Mean is that value of a given static data or for a data set, which is the sum of the values divided by the number of values. the arithmetic mean, also called the expected value or average value of any set number.

Mean can be calculated by various method like Direct method, Assumed-Mean method, Step-Deviation method, etc. every student study all these types of method in class 10.

What is Median?

Median is defined as the middle value for a data set. In statistics the median is the value separating the higher half from the lower half of a given data.

What is Mode?

It is that value of a variate which occurs most often. More precisely, mode is that value of the variable at which the concentration of the data is maximum.

5 plus Example Question Using the Mean, Median and Mode Relationship.

Sure! Here's an example question using the relationship between the mean, median, and mode:

Question:

In a class, the ages of 7 students are as follows: 12, 15, 16, 17, 18, 18, 19.

What is the mean age of the students?
What is the median age?
What is the mode of the ages?

Now, let's use the relationship between mean, median, and mode:

If the data is roughly symmetric, the mean, median, and mode are often close to each other.
If the data is skewed, the mean will be pulled in the direction of the skew.

Answer:

Mean:
Sum of ages = 12 + 15 + 16 + 17 + 18 + 18 + 19 = 115
Mean = 115 / 7 = 16.43 (approximately)
Median:
Since the data is ordered (12, 15, 16, 17, 18, 18, 19), the median is the middle value: 17.
Mode:
The mode is the value that appears most frequently. Here, 18 appears twice, so the mode is 18.

Relationship Insight:

The mean (16.43), median (17), and mode (18) are close, but the mean is slightly lower than the median and mode, indicating that the data might be slightly skewed to the left (lower values are pulling the mean down).

Certainly! Here are five more examples using the relationship between the mean, median, and mode:

Example 1:

Ages of 9 children in a family: 4, 6, 7, 7, 8, 10, 10, 12, 14.

Mean:
Sum of ages = 4 + 6 + 7 + 7 + 8 + 10 + 10 + 12 + 14 = 78
Mean = 78 / 9 = 8.67
Median:
Ordered data: 4, 6, 7, 7, 8, 10, 10, 12, 14.
The middle value is the 5th number: 8.
Mode:
The mode is the number that appears most often: 7 and 10 both appear twice.
So, the data is bimodal: 7 and 10.

Relationship Insight:
The mean (8.67) is greater than the median (8), suggesting a slight right skew, where higher values (10, 12, 14) are pulling the mean up.

Example 2:

Scores of 6 students in a test: 45, 50, 55, 55, 60, 80.

Mean:
Sum of scores = 45 + 50 + 55 + 55 + 60 + 80 = 345
Mean = 345 / 6 = 57.5
Median:
Ordered data: 45, 50, 55, 55, 60, 80.
The median is the average of the 3rd and 4th numbers: (55 + 55) / 2 = 55.
Mode:
The mode is the value that appears most often: 55.

Relationship Insight:
The mean (57.5) is greater than the median (55), suggesting a slight right skew due to the outlier (80).

example 3:

Monthly salaries (in $1000) of 5 employees: 30, 35, 40, 42, 90.

Mean:
Sum of salaries = 30 + 35 + 40 + 42 + 90 = 237
Mean = 237 / 5 = 47.4
Median:
Ordered data: 30, 35, 40, 42, 90.
The middle value is the 3rd number: 40.
Mode:
There is no repeated salary, so no mode.

Relationship Insight:
The mean (47.4) is significantly higher than the median (40), indicating a strong right skew, likely due to the outlier salary of 90

Example 4:

Heights (in cm) of 8 people: 150, 160, 160, 165, 170, 170, 180, 200.

Mean:
Sum of heights = 150 + 160 + 160 + 165 + 170 + 170 + 180 + 200 = 1455
Mean = 1455 / 8 = 181.875
Median:
Ordered data: 150, 160, 160, 165, 170, 170, 180, 200.
The median is the average of the 4th and 5th numbers: (165 + 170) / 2 = 167.5.
Mode:
The mode is the value that appears most often: 160 and 170.

Relationship Insight:
The mean (181.88) is much higher than the median (167.5), suggesting a strong right skew, which is likely influenced by the outlier of 200.

Example 5:

Number of books read by 10 students: 3, 5, 6, 7, 7, 8, 8, 8, 9, 10.

Mean:
Sum of books = 3 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9 + 10 = 77
Mean = 77 / 10 = 7.7
Median:
Ordered data: 3, 5, 6, 7, 7, 8, 8, 8, 9, 10.
The median is the average of the 5th and 6th numbers: (7 + 8) / 2 = 7.5.
Mode:
The mode is the value that appears most often: 8.

Relationship Insight:
The mean (7.7) is slightly greater than the median (7.5), indicating that the distribution is slightly right-skewed.T

hese examples demonstrate how the relationship between the mean, median, and mode can provide insights into the distribution of the data, particularly in terms of skewness or symmetry.

What is the mean, median, and mode of 13 16 12 14 19 12 14 13 14?

Mean:-

Sum of the values:

13 + 16 + 12 + 14 + 19 + 12 + 14 + 13 + 14 = 117

Number of values:
There are 9 values in the dataset.

\text{Mean} = \frac{117}{9} = 13

So, the mean is 13.

Median:-

arrange the numbers in ascending order and then find the middle number.

Sorted data:

$12, 12, 13, 13, 14, 14, 14, 16, 19$

Since there are 9 numbers (an odd number), the median is the number in the middle position, which is the 5th value.

So, the median is 14.

Mode:-

The mode is the number that appears most frequently in the dataset.

From the sorted data, we see that:

12 appears 2 times,
13 appears 2 times,
14 appears 3 times,
16 appears 1 time,
19 appears 1 time.

Since 14 appears the most (3 times), the mode is 14.

Final Answer:

Mean = 13
Median = 14
Mode = 14

What is the median of 3 7 2 4 7 5 7 1 8 8?

To find the median of the dataset

3 7 2 4 7 5 7 1 8 8

Sorted data:

1,2,3,4,5,7,7,7,8,8

Since there are 10 values (an even number), the median will be the average of the 5th and 6th values.

The 5th value is 5
The 6th value is 7

Median = \frac{5 + 7}{2} = \frac{12}{2} = 6

The median is 6.

What is the mean, median, and mode of the following data: 5, 10, 10, 12, 13?

Mean:- The mean is calculated by adding all the numbers together and then dividing by the number of values in the dataset.

Sum of the values:

5 + 10 + 10 + 12 + 13 = 50

Number of values: There are 5 values in the dataset.

\text{Mean} = \frac{50}{5} = 10

So, the mean is 10.

Median:-

To find the median, we need to arrange the numbers in ascending order (although they are already in order) and find the middle value.

Sorted data:

$5, 10, 10, 12, 13$

Since there are 5 values (an odd number), the median is the middle value, which is the 3rd value in this sorted list.

So, the median is 10.

Mode:-

The mode is the number that appears most frequently in the dataset.

In this case:

$5$ appears 1 time,
$10$ appears 2 times,
$12$ appears 1 time,
$13$ appears 1 time.

Since 10 appears the most (2 times), the mode is 10.

Final answer

Mean = 10
Median = 10
Mode = 10

What is the median of 21 62 66 66 79 28 63 48 59 94 19?

Sorted data:

19,21,28,48,59,62,63,66,66,79,94 (Arranged in ascending order)

Now find the middle term,

Since there are 11 numbers (an odd number), the median is the middle value.

The middle value is the 6th value in the sorted list.

Median = 62

Final answer

The median is 62.

What is the median of 2 3 4 5 1 2 3 4 6 5?

Sorted data:

Arrange in Ascending order

$1, 2, 2, 3, 3, 4, 4, 5, 5, 6$

Since there are 10 numbers (an even number), the median will be the average of the 5th and 6th values.

The 5th value is $3$ , and the 6th value is $4$ .

$\text{Median} = \frac{3 + 4}{2} = \frac{7}{2} = 3.5$

Median=23+4=27=3.5

$Final answer$

The median is 3.5.

What is the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10?

To find the mode of the dataset $10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10$ , follow these steps:

1. Count the frequency of each number:

$10$ appears 3 times
$12$ appears 1 time
$11$ appears 2 times
$15$ appears 1 time
$20$ appears 1 time
$19$ appears 1 time
$21$ appears 1 time
$9$ appears 1 time

2. Identify the most frequent number:

The number that appears the most is 10, which appears 3 times.

Final answer

The mode is 10.

What is equal to 3 median 2 mean?

median = mode + 2 mean.

3 median 2 mean equal to mode.

Aditya Raj Anand

Define Inertia of motion with 10 visual examples, formula and Application

Physics

After a long discussion on Inertia of rest. The time has come to talk about inertia of motion. Not only the definition but also 10 examples of inertia of motion that we have all experienced in our day to day life.

But before we go further, let's make a table of contents for this post.

Topic covered in this lecture

What is an Inertia of motion?
Formula of inertia of motion.

Q. What is inertia give an example of inertia of motion also explain which of the following has more inertia an empty box or a box full of books?

Daily life examples of inertia of motion with visual picture.
Application of inertia of motion.
Where is Inertia of motion came from?
Why inertia of motion related to Newton's first law of motion?

All the above topic are well explained in the following notes. So let's start.

What is inertia of motion?

If we talk about only inertia, neither rest nor motion. Then it is a tendency of a body to keep their original state.

So, Inertia of motion is defined as the tendency of a body to keep their original state of motion forever. Untill or unless an external force is applied to it.

Please note that :- In inertia of motion, the direction of the moving object also constant. Means will be moving in only one direction forever.

Let's take an example to understand the inertia of motion more clearly.

Case 1:-

Suppose a car is running on a straight road at a speed of 40 km/h. After 5 hours of constant moving, a curve turning has come. Now, if we didn't apply the external force (or brake) the car will be accident.

But if we apply the brake to the car, suddenly we feel a forward jerk. This jerk is because of inertia of motion.

This explains as follows : When we apply the brake the car has stopped but our body has a tendency to keep their original state of motion. Due to this we feel jerk in the forward direction.

Case 2:-

Suppose the same car is running on a straight road at a speed of 40 km/h. After 3 hours of constant moving a road breaker has come.

Now, when the car cross the breaker, the wheel of the car leave the ground for some minor second and after that it again touches the ground. But due to this we felt a jump inside the car.

This jump is because of inertia of motion. This explains as follows:

While the constant moving of the car. Our body is in state of rest with respect to other person inside the car. But in motion with respect to the people who has seen from outside the car.

Please note that :- This case is also a good example of rest and motion are relative terms.

So, after crossing the road breaker our body gain some motion but after some micro second it again touches the ground. So we felt jump in upward direction.

Case 3:-

Suppose, we are sitting in the same car. After some time, if we change the direction of the car. We felt down in the right side because of the inertia of direction.

Rest and motion are relative terms.

Suppose a person is standing on the moon. We can say that person is in state of rest with respect to another person stand beside them. But in motion with respect to that person who seen both of them from earth.

Let's take another example to illustrate our above example.

Suppose we are sitting on a running train. Here we can say that we are in state of rest with respect to other passages sitting besides us. But we are still in motion with respect to the passages standing on the platform.

formula of inertia of motion

Please note that there is no definite formula to calculate the inertia of motion, rest or direction.

Inertia is a phenomenon in science. It is not a mathematical concepts or equations.

The inertia of momentum has a formula. But not inertia of motion.

Inertia of motion is used to understand the concept of the questions. Inertia can be used to clean the concept of Newton's first law of motion.

Q. What is inertia give an example of inertia of motion also explain which of the following has more inertia an empty box or a box full of books?

In most simple words, Inertia is the tendency or behaviour of a body that helps them to keep their original state unless or until an external force is applied to it.

Please not that the body may be in state of rest or motion.

Example of inertia of motion.

Applying brake suddenly when the car is in motion. This explains as follows:

When the car is moving in a straight line at constant speed. And if we apply the brake, it goes slow down and Stop after some time. Due to the inertia of motion. Because the moving car always wants to remains in motion as according to Newton's first law. But when we apply brake, Newton's law break. That's the reason we feel forward force after applying brake.

Now, the question is which has more inertia.

1. An empty box.

2. A box with full of books.

Hence, to answer this question. Let's first understand that the object which has more masses has more inertia than the lighter one.

So, here the box full of books has more inertia than the empty box.

Daily life examples of inertia of motion with visual picture

Feel backward force when car suddenly start.
Feel forward force when car suddenly stops.
Collision of moving objects in space.
Moving of satellite in space.
Moving of planets in space.
Jump from moving train.
Objects come to you when throw inside the moving train.
Athletes not stop running even after reach to the final position.
The moving of bike for some time, even we off the engine.
Continuous moving of stone attached with thread in circular path.

These are the 10 most common and familiar examples of inertia of motion that we have expressed in our life.

1. Feel backward force when car suddenly start.

When a car suddenly starts, you feel a backward force because of inertia, which is a property of matter described by Newton's First Law of Motion. Here's an explanation of why this happens:

Inertia is the tendency of an object to resist changes in its state of motion. According to Newton's First Law, an object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an external force.

When you are sitting in the car at rest and the car suddenly accelerates forward:

The car starts moving forward, but your body, which was initially at rest, tends to stay in the same position because of inertia.

To compensate for the sudden acceleration, your body resists the forward motion, which causes you to feel as if you're being pushed backward relative to the car.

2.Feel forward force when car suddenly stops.

When a car suddenly stops, you feel a forward force due to inertia, which is a consequence of Newton's First Law of Motion. Here's why this happens:

Inertia and Newton’s First Law of Motion

Inertia is the tendency of an object to resist changes in its state of motion. According to Newton's First Law, an object will remain in its current state of motion (whether at rest or moving) unless acted upon by an external force.

When the car suddenly stops:

The car decelerates (slows down) quickly, but your body, which was moving forward with the car, wants to keep moving at the same speed because of its inertia.

Since your body tends to keep moving forward while the car is now decelerating, you feel as if you are being pushed forward.

Understanding the Force

As the car comes to a sudden stop, it exerts a backward force on you (via the seat and seatbelt).

Your body resists the sudden deceleration and wants to continue moving forward.

The forward force you feel is your body’s resistance to this change in motion. Essentially, you're trying to maintain the forward velocity that you had before the car stopped, and this results in the sensation of being pushed forward.

This is why you feel like you're being pushed forward when the car suddenly stops. The seatbelt or any other restraint system in the car works to counteract this forward motion by applying a backward force to bring your body to a stop along with the car.

3. Collision of moving objects in space.

Collisions between moving objects in space can occur in a variety of scenarios, such as the collision of asteroids, comets, spacecraft, or even smaller particles like space debris. These collisions are governed by the basic principles of physics, including momentum conservation, energy conservation, and the laws of motion.

Key Concepts in Collisions of Moving Objects in Space:

Conservation of Momentum: In an isolated system, where no external forces are acting, the total momentum before the collision is equal to the total momentum after the collision. This is a fundamental principle known as conservation of momentum. Momentum ( $p$ ) is the product of an object's mass and its velocity ( $p = mv$ ).
- If two objects collide in space, their combined momentum before and after the collision remains the same, assuming no external forces (like gravity or friction) are involved during the brief time of the collision.
Conservation of Energy: In the case of elastic collisions, both kinetic energy and momentum are conserved. However, in inelastic collisions, while momentum is conserved, some of the kinetic energy is transformed into other forms of energy, such as heat, sound, or deformation (like crumpling in the case of spacecraft).
- In space, the lack of air resistance means that energy lost as heat or sound might not dissipate in the same way as on Earth, but energy still gets converted into other forms (e.g., deformation of objects or the production of heat).
Types of Collisions:
- Elastic Collision: Both momentum and kinetic energy are conserved. After the collision, the objects bounce off each other without any permanent deformation. This is a rare occurrence in space since most space objects are not perfectly rigid.
- Inelastic Collision: Momentum is conserved, but kinetic energy is not. Some energy is lost, and the objects may deform or break apart. For example, when two asteroids collide, they might break into fragments, and the fragments might continue to move with the combined momentum of the original objects.
- Perfectly Inelastic Collision: This is the extreme case where the colliding objects stick together after the collision, moving as one mass with the combined momentum. This type of collision is also common when large objects like asteroids collide, often resulting in the formation of a new, single object.
Force of Impact: The force experienced during a collision depends on the change in momentum and the duration of the collision. In space, objects like asteroids or comets have extremely high velocities, so even a seemingly small change in velocity can result in a significant release of energy.
Relativistic Effects: In high-speed collisions (i.e., when objects approach significant fractions of the speed of light), relativistic effects become important. In such cases, both momentum and energy must be considered in the relativistic form, which takes into account the increase in mass as an object approaches the speed of light.

Example: Collision of Asteroids in Space

Suppose two asteroids are on a collision course, moving at velocities $v_1$ and $v_2$ , and have masses $m_1$ and $m_2$ , respectively. The total momentum before the collision would be:
$p_{\text{total}} = m_1 v_1 + m_2 v_2$
After the collision, if the asteroids collide elastically, the velocities change, but the total momentum remains the same. However, if the collision is inelastic, the kinetic energy will be partially converted into other forms of energy, such as heat or deformation.

Outcome of Collisions in Space

Creation of Craters: The collision of large objects (like asteroids) can create craters on planets or moons, as seen in Earth's history with the impact that contributed to the extinction of the dinosaurs.
Fragments and Debris: If objects collide with high velocity, they may break into smaller fragments. These fragments could continue to move through space, potentially causing further collisions.
Spacecraft Collisions: In the case of spacecraft, a collision could be catastrophic. Spacecraft and satellites often take precautions to avoid collisions with space debris, which can cause significant damage at high speeds, despite the lack of atmosphere in space.

Conclusion

Collisions in space, although occurring in the vacuum of space where there is no air resistance, still obey fundamental physical laws, particularly the conservation of momentum and energy. The outcomes of these collisions depend on the types of objects involved, their velocities, and the nature of the collision. The lack of atmospheric drag means that objects continue moving with high velocities post-collision, which could lead to lasting effects like fragmentation or the creation of new objects.

4. Moving of satellite in space.

Satellites in space move according to the principles of orbital mechanics, primarily governed by the gravitational force and centripetal force. Here’s an explanation of how satellites move in space:

1. Orbital Motion and Gravitational Force

A satellite in orbit around a planet or other celestial body is essentially in free fall, constantly being pulled toward the planet by gravity. However, its tangential velocity (speed in a direction perpendicular to the force of gravity) keeps it from falling directly to the surface.

The gravitational force between the planet and the satellite provides the centripetal force that keeps the satellite in orbit.

Inertia causes the satellite to move in a straight line unless acted upon by an external force, while gravity continually pulls the satellite toward the planet, creating a curved path. This balance of forces results in the satellite continuously "falling" around the planet, maintaining its orbit.

5. Moving of planets in space.

Inertia: According to Newton’s First Law of Motion, an object in motion tends to remain in motion at a constant velocity unless acted upon by an external force. In the case of a planet, its inertia wants it to move in a straight line, but the Sun’s gravitational pull prevents it from flying off into space.

Thus, planets move in orbits, constantly falling towards the Sun due to gravity, but their inertia causes them to keep moving forward, creating an elliptical orbit.

6. Jump from moving train.

Jumping from a moving train is extremely dangerous and should be avoided at all costs. However, understanding the physics behind it helps explain why it’s so risky. Here’s what happens:

When you're inside a moving train, you are moving at the same speed as the train, relative to the ground outside. If the train is moving at 50 km/h, you, along with everything inside, are also moving at 50 km/h in the same direction as the train.

Relative to the train: You are stationary in the train.

Relative to the ground: You are moving at the same speed as the train.

When you jump off the train, your body still retains the horizontal speed of the train (50 km/h, for example) at the moment you leave it, since there is no external force to stop that horizontal motion immediately.

What Happens When You Jump Off : At the moment you jump, you maintain the horizontal velocity of the train. This means that even after leaving the train, you will still be moving forward at the same speed as the train (unless air resistance or friction acts on you).

7. Objects come to you when throw inside the moving train.

In a moving train, if you throw an object backward, it might appear to come toward you relative to your position inside the train, because you and the object are both moving forward at the same speed as the train. However, relative to the ground outside, the object retains the train's speed (forward or backward), and its motion is adjusted accordingly.

When you throw an object inside a moving train, the behavior of the object depends on the relative motion between you, the train, and the object.

8. Athletes not stop running even after reach to the final position.

Athletes continue running even after reaching the finish line due to their inertia, momentum, and the need for gradual deceleration to avoid injury. The combination of physiological and psychological factors means that it takes a moment for them to stop, even after they've crossed the final position in a race.

When athletes run in a race and continue running even after reaching the final position, it’s due to several factors related to inertia, momentum, and reaction to the environment. Here's an explanation of why this happens:

Inertia and Momentum :-

Inertia is the tendency of an object to resist changes in its motion. According to Newton's First Law of Motion, an object in motion will stay in motion unless acted upon by an external force.

When an athlete is running at high speed, they have momentum — the product of their mass and velocity. Even if they reach the finish line, their body will want to continue moving due to inertia, which means they will keep running for a brief moment after crossing the finish line.

9. The moving of bike for some time, even we off the engine.

When a bike continues to move for some time even after the engine is turned off, it is due to the concept of inertia and the momentum of the bike. Here's an explanation of what happens:

Inertia and Momentum :- Inertia: According to Newton’s First Law of Motion, an object in motion will remain in motion unless acted upon by an external force. In the case of the bike, the inertia of the bike's motion makes it continue moving even after the engine is turned off.

Momentum: The bike has momentum — the product of its mass and velocity. When the engine is running, the bike gains momentum as it moves forward. Even after you turn off the engine, the bike retains this momentum and will continue moving forward for a while until external forces (like friction, air resistance, and the brakes) slow it down.

10. Continuous moving of stone attached with thread in circular path.

Inertia of the Stone :- The stone has inertia, which is its tendency to resist changes in motion. If there were no force acting on it, the stone would move in a straight line tangent to the circular path at any point.

However, because the thread pulls the stone toward the center, it prevents the stone from flying off in a straight line. The result is that the stone moves in a circular path instead.

Application of inertia of motion.

Application of car brakes, train brakes etc works on the inertia of motion.

The runner athelete also uses the application of inertia of motion for long jumping.

The scientist also uses the application of inertia of motion in space satellite.

The study of the motion of earth and other planets can be understood by the application inertia of motion.

Aeroplane take off and landing is also use application of inertia of motion.

Why inertia of motion related to Newton's first law

According to Newton's first law of motion, a rest body always remains in state of rest and a moving object always in state of motion.

Hence, inertia of motion said that, a body which is moving with some velocity. It always moving forever until or unless an external force is applied to it.

So, the definition of both the term are inter relative. Not only the definition but also the concept of both the terms are co-related.

Aditya Raj Anand