Looking for a Tutor Near You?

Post Learning Requirement »
x

Choose Country Code

x

Direction

x

Ask a Question

x

x
x
For better view click here
x
Hire a Tutor
DISCOVER

Average - Basic & Change In Average

Loading...

Published in: Mathematics
1,304 Views

Solve Change in Average problems within seconds

Kumar / Kolkata

7 years of teaching experience

Qualification: B.Tech/B.E. ( - 2010)

Teaches: Algebra, Economics, Mathematics, Social Studies, CSAT, IBPS, SSC Exams, UPSC Exam, Electronics

Contact this Tutor
  1. Average- Basic & Change in Average calculation Average is the one of most important topic asked in every aptitude exam and has application in different problems of quantitative aptitude. "Average= Sum of observations / No. of observations" This is the most basic definition of average used in everyday problems. Simple.. But problems are not asked this straightforward. So, we need to understand the asl concept of Average, so as to solve the twisted problems easily. Concept of Average:- Students Total Age 27 29 23 20 21 24 144 Average age 24 24 144 Difference of Age and Avera e a e 3 5 -1 -4 -3 O O Note from table:- 1. The s m tota of individual ages and average ages is same. From this, we can easily conclude that " Each student can be assumed to be of age= 24 years" . This concept (assum tion) IS very useful in solving average problems. It means that we can assume that each item is equal to their average. 2. In the last column -"difference of Individual's age and average age", the cumulative sum is zero. This is always the case. Example • Calculate average of 3629, 3745, 3842, 3361, 3473. Method:- Since these are 4 digits numbers, we go by Average assumption method. 1. 2. 3. Assume an average = 3600 (since largest number= 3842, smallest number= 3361. And 3600 is approx middle of largest and smallest number). Now, take difference of each from the average. (Number — Average) (3629-3600), (3745-3600), (3842-3600), (3361-3600), (3473-3600) = 29, 145, 242, -239, -127 Now take cumulative sum = 29+145+242+(-239)+(-127) = +50 By- Kumar Member Id -- MPT 240463
  2. 4. 5. Since, cumulative sum is +50. This implies that actual average is (+50/5) more than assumed average (3600). Therefore, Actual average = 3600 + 10 = 3610. Properties of Average Here I will give some important properties related to average calculation which Tv&ill help you in problem sol\ing. If each quantity (or item) is either increased (or decreased) by a certain value, then iheir new 1. average is also increased (or decreased) by same value. 2. If each quantity (or item) is either multiplied (or divided) by a certain value, then their new average is also multiplied (or divided) by same value. Example 1: The average of 8 numbers is 12. If each number is multiplied y then 7 is added to each of them, then the new average is?? Solution: Stepl: First multiplied by 9. Therefore, new average = 2 * 9 108' Step2: 7 is added. Therefore, new average = 108 + 7 = 115. Single Step: New average = (12*9) +7 = 115. Example 2: The average age of a class of 50 students is 15 y€9rs. 3 years later, the average age of the same class of 50 students is?? Solution: New average age = 15 + 3 —18 years. (Since 3 years is added to each of the students' age). Example 3: The average age of famil 5 members 4 years ago was 40 years. Two years ago a new baby was born in thi fami . F!ve years later the average age of the family will be?? Solution: New average = {(40+9)*5}+7}/6 = 42 years. Explanation: Stepl: Average agegf 5 members after five years = 40+9 = 49 YTS. (since 40 was average 4 years ago. Therefore, five years later => 4+5 = 9 years). Step2. Age of baby five years later = 7 years (As baby was born 2 years ago). SV3.Ap!al age = 49*5 + 7 = 252 years. Ste 4: Therefore, Average age = 252/6 = 42 (Now 6 members including baby). Note The same question can be misted like:"The average age of a family of 5 members is 49 years. On inclusion of a baby in the family, the average age decreased to 42 years. What is the age I will give a detailed explanation of this in another note and also related concept. Till then practice problems on Average applying above concepts. If you have any queries, do mite to me. By- Kumar Member Id -- MPT 240463

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related Study Notes

Upload Study Notes

If you have your own Study Notes which you think can benefit others, please upload on LearnPick. For each approved Study Note you will get 100 Credit Points and 100 Activity Score which will increase your profile visibility.

Upload Now
Home > Study Notes > Average - Basic & Change In Average