Average Or Ap

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Average

What is Average?

The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.

The main term of average is equal distribution of a value among all which may distribute persons or things. We obtain the average of a number using formula that is sum of observations divided by Number of observations.

Here is average based some fact and formula and some average shortcut tricks examples. The problem is given in Quantitative Aptitude which is a very essential paper in ssc exam. Given below are some more example for practicing.

Formula:

• Average: = (Sum of observations / Number of observations).

Find the Average Speed

• If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by-   
• If a person covers A km at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is- 

When a person leaves the group and another person joins the group in place of that person then-

• If the average age is increased,
  Age of new person = Age of separated person + (Increase in average × total number of persons)
• If the average age is decreased,
  Age of new person = Age of separated person – (Decrease in average × total number of persons)

When a person joins the group-In case of increase in average

• Age of new member = Previous average + (Increase in average × Number of members including new member)

In case of decrease in average

• Age of new member = Previous average – (Decrease in average × Number of members including new member)

In the Arithmetic Progression there are two cases when the number of terms is odd and second one is when number of terms is even.

• So when the number of terms is odd the average will be the middle term.
• when the number of terms is even then the average will be the average of two middle terms.

Some Important Examples

Examples 1: what will be the average of 13, 14, 15, 16, 17?

Solution: Average is the middle term when the number of terms is odd, but before that let’s checks whether it is in A.P or not, since the common difference is same so the series is in A.P. So the middle term is 15 which is our average of the series.

Example 2: What will be the average of 13, 14, 15, 16, 17, 18?

Solution: We have discussed that when the number of terms are even then the average will be the average of two middle terms.

Now the two middle terms are 15 and 16, but before that the average we must check that the series should be A.P. Since the common difference is same for each of the term we can say that the series is in A.P. and the average is (16+15)/2 = 15.5

Example 3:The average of five numbers is 29. If one number is excluded the average becomes 27. What is the excluded number ?

Answer :

let the excluded number is

= (29 x 5) – ( 27 x 4 )

= 145 – 108

= 37 .

Example 4: Find the average of first 20 natural numbers?

Answer:

Sum of first n natural numbers = n ( n + 1 ) /2

So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210

So, then Required average is = 210 / 20 = 10.5.

Example 5

Find the average of first 20 multiplies of 5 .

Answer:

Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20

= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5 .

So the Required average is 52.5.

Questions:

Level-I:

Answers:

Level-I:

Answer:1 Option A

Explanation:

Answer:2 Option B

Explanation:

Answer:3 Option A

Explanation:

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

 Required sale = Rs. [ (6500 x 6) – 34009 ]

   = Rs. (39000 – 34009)

   = Rs. 4991.

Answer:4 Option D

Explanation:

Average of 20 numbers = 0.

 Sum of 20 numbers (0 x 20) = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

Answer:5 Option C

Explanation:

Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

Answer:6 Option A

Explanation:

Let the average age of the whole team by x years.

 11x – (26 + 29) = 9(x -1)

 11x – 9x = 46

 2x = 46

 x = 23.

So, average age of the team is 23 years.

Answer:7 Option B

Explanation:

Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5050 x 2) = 10100 …. (i)

Q + R = (6250 x 2) = 12500 …. (ii)

P + R = (5200 x 2) = 10400 …. (iii)

Adding (i), (ii) and (iii), we get:  2(P + Q + R) = 33000  or   P + Q + R = 16500 …. (iv)

Subtracting (ii) from (iv), we get P = 4000.

• P’s monthly income = Rs. 4000.

Answer:8 Option B

Explanation:

Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.

 Husband’s present age = (90 – 50) years = 40 years.

Answer:9 Option A

Explanation:

Total amount spent = Rs. (3 x 4000) = Rs. 12000.

Answer:10 Option A

Explanation:

Let Arun’s weight by X kg.

According to Arun, 65 < X < 72

According to Arun’s brother, 60 < X < 70.

According to Arun’s mother, X <= 68

The values satisfying all the above conditions are 66, 67 and 68.

Level-II:

Answer:11 Option D

Explanation:

Let A, B, C represent their respective weights. Then, we have:

A + B + C = (45 x 3) = 135 …. (i)

A + B = (40 x 2) = 80 …. (ii)

B + C = (43 x 2) = 86 ….(iii)

Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)

Subtracting (i) from (iv), we get : B = 31.

 B’s weight = 31 kg.

Answer:12 Option C

Explanation:

Answer:13 Option D

Explanation:

Since the month begins with a Sunday, to there will be five Sundays in the month.

Answer:14 Option B

Explanation:

Answer:15 Option C

Explanation:

Let there be x pupils in the class.

Answer:16 Option D

Explanation:

P + Q + R + S = (30 x 4)      P + Q + R + S = 120 …. (i)

 I. P + R = 60 …. (ii)

II. S = (R – 10) …. (iii)

From (i), (ii) and (iii), we cannot find R.

 Correct answer is (D)

Answer:17 Option B

Explanation:

 I. Total candidates interviewed by 3 panels = (15 x 3) = 45.

II. Let x candidates be interviewed by C.

Number of candidates interviewed by A = (x + 2).

Number of candidates interviewed by B = (x + 1).

 x + (x + 2) + (x + 1) = 45

 3x = 42

 x = 14

Hence, the correct answer is (B).

Answer:18 Option D

Explanation:

Let there be x children.

I gives, age of teacher = x years.

II gives, average age of (x + 1) persons = (x + 1) years.

 Teacher’s age = (x + 1) (x + 1) – x² = (x² + 1 + 2x) – x² = (1 + 2x)

Thus, teacher’s age cannot be obtained.

 Correct answer is (D)

,

Advanced Placement (AP) courses are college-level courses that are offered to high school students. AP courses are designed to be more challenging than regular high school courses, and they can be used to earn college credit.

There are many different AP courses available, covering a wide range of subjects. Some of the most popular AP courses include AP Calculus AB and BC, AP Computer Science A and AP Computer Science Principles, AP English Language and Composition, AP English Literature and Composition, AP European History, AP Macroeconomics, AP Microeconomics, AP Physics 1 and 2, AP Statistics, AP United States Government and Politics, and AP United States History.

AP courses are typically offered during the junior and senior years of high school. To take an AP course, students must typically have a good academic record and be able to demonstrate that they are prepared for the rigors of college-level work.

AP courses are not easy, but they can be very rewarding. If you are a high school student who is looking for a challenge and want to earn college credit, then AP courses may be a good option for you.

Here is a more detailed look at some of the most popular AP courses:

• AP Calculus AB and BC: These courses cover the basics of calculus, including limits, Derivatives, integrals, and infinite series. AP Calculus AB is a one-year course, while AP Calculus BC is a two-year course.
• AP Computer Science A: This course covers the Basics of Computer science, including programming, data structures, and algorithms.
• AP English Language and Composition: This course covers the basics of writing, including grammar, punctuation, style, and argument.
• AP English Literature and Composition: This course covers the basics of literature, including analysis, interpretation, and critical thinking.
• AP European History: This course covers the history of Europe from the ancient Greeks to the present day.
• AP Macroeconomics: This course covers the basics of macroeconomics, including economic Growth, Inflation, and Unemployment.
• AP Microeconomics: This course covers the basics of microeconomics, including supply and demand, market equilibrium, and consumer choice.
• AP Physics 1 and 2: These courses cover the basics of physics, including mechanics, Magnetism/”>Electricity and Magnetism, and waves.
• AP Statistics: This course covers the basics of statistics, including Probability, data analysis, and inference.
• AP United States Government and Politics: This course covers the basics of American government and politics, including the Constitution, the three branches of government, and public policy.
• AP United States History: This course covers the history of the United States from the colonial period to the present day.

If you are interested in taking an AP course, be sure to talk to your guidance counselor or AP teacher. They can help you determine which courses are right for you and how to prepare for them.

Taking AP courses can be a great way to challenge yourself academically and earn college credit. If you are up for the challenge, then AP courses may be a good option for you.

What is the difference between average and AP?

Average is a general term that refers to a typical or usual amount, level, or degree. AP, on the other hand, is a specific term that refers to Advanced Placement courses and exams. AP courses are college-level courses that are offered in high school, and AP exams are standardized tests that students can take to earn college credit.

What are the benefits of taking AP courses?

There are many benefits to taking AP courses, including:

• The opportunity to earn college credit: AP exams are scored on a scale of 1 to 5, and students who earn a score of 3 or higher can earn college credit for the course. This can save students time and Money in college.
• The opportunity to challenge yourself academically: AP courses are more challenging than regular high school courses, and they can help you develop the skills you need to succeed in college.
• The opportunity to gain access to exclusive scholarships: Some scholarships are only available to students who have taken AP courses.

What are the challenges of taking AP courses?

AP courses are more challenging than regular high school courses, and they can be demanding on your time and energy. However, the benefits of taking AP courses can outweigh the challenges.

What are some tips for success in AP courses?

Here are some tips for success in AP courses:

• Start early: Don’t wait until the last minute to start studying for AP exams. Start early and give yourself plenty of time to review the material.
• Create a study schedule: Create a study schedule and stick to it. Make sure to schedule time each week to review the material for your AP exams.
• Find a study buddy: Studying with a friend can help you stay motivated and accountable.
• Take practice tests: Taking practice tests can help you get familiar with the format of the AP exams and identify areas where you need to improve.
• Get enough sleep: Getting enough sleep is essential for success in any course, but it’s especially important for AP courses.
• Eat healthy foods: Eating healthy foods will give you the energy you need to focus and succeed in your AP courses.
• Exercise regularly: Exercise is a great way to reduce Stress and improve your focus.
• Take breaks: Don’t try to study for hours on end without taking a break. Get up and move around every 20-30 minutes to avoid getting too stressed or overwhelmed.
• Believe in yourself: The most important thing is to believe in yourself and your ability to succeed in AP courses. If you put in the time and effort, you can achieve your goals.

Sure, here are some multiple choice questions without mentioning the topic Average or AP:

1. What is the sum of the first 10 natural numbers?
   (A) 55
   (B) 50
   (C) 45
   (D) 40

2. What is the average of 1, 2, 3, 4, and 5?
   (A) 3
   (B) 4
   (C) 5
   (D) 6

3. What is the Median of 1, 2, 3, 4, and 5?
   (A) 2
   (B) 3
   (C) 4
   (D) 5

4. What is the mode of 1, 2, 3, 4, and 5?
   (A) 1
   (B) 2
   (C) 3
   (D) 4

5. What is the range of 1, 2, 3, 4, and 5?
   (A) 4
   (B) 5
   (C) 6
   (D) 7

6. What is the standard deviation of 1, 2, 3, 4, and 5?
   (A) 1.224746
   (B) 1.414213
   (C) 1.732050
   (D) 2.236068

7. What is the Variance of 1, 2, 3, 4, and 5?
   (A) 1.224746
   (B) 1.414213
   (C) 1.732050
   (D) 2.236068

8. What is the coefficient of variation of 1, 2, 3, 4, and 5?
   (A) 0.4472136
   (B) 0.5000000
   (C) 0.5773502
   (D) 0.6180339

9. What is the skewness of 1, 2, 3, 4, and 5?
   (A) 0
   (B) 0.25
   (C) 0.50
   (D) 0.75

10. What is the kurtosis of 1, 2, 3, 4, and 5?
    (A) 3
    (B) 2.5
    (C) 1.5
    (D) 0.5

I hope these questions are helpful!