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# Averages online

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• There is not much to talk of on percentages, state the obvious and go on to 1-2 examples.
• There is not much to talk of on percentages, state the obvious and go on to 1-2 examples.
• This is a brilliant framework. It works for almost all questions. For the next 5-6 questions, use this framework.
• ### Averages online

1. 1. 2IIM Ascent Education’s An IIM Alumni Venture Mean Median • Teaching Notes – Ascent Education
2. 2. 2IIM Ascent Education’s An IIM Alumni Venture Theory Averages – Basic concepts 2 Average is a measure that gives a general idea about a sample space. The formula for computing average is straight-forward : Average = One basic example What is the average score in 5 subjects if you score 44, 56, 72, 60 and 28 in them? Critical skill set - To get average from total, total from average, number of entities given both. objectsofnumberTotal Total
3. 3. 2IIM Ascent Education’s An IIM Alumni Venture Theory Averages – Weighted average  Normal average assumes that all measurements have equal weightages. But we can attach different weights to each measurement as well. Weighted average formula is as follows.  Average A = , where w1 and w2 are weightages and a1 and a2 are averages are the respective averages One basic example  Average weight of 20 boys in a class is 50 kgs. Average weight of 30 girls in the same class is 40 kgs. What is the overall average weight Overall average = = 44 kgs. 3 3020 40*3050*20 + + 21 2211 ww awaw + +
4. 4. 2IIM Ascent Education’s An IIM Alumni Venture Theory Averages – Standard framework 4 Example question: The average age of the students of a class A comprising 30 students is 16 years and that of class B comprising 20 students is 11 years. What is the average age of the students of the two classes taken together? Number * Average = Total 30 16 480 20 11 220 50 = 14 700 50 700
5. 5. 2IIM Ascent Education’s An IIM Alumni Venture Question The average revenue of company A in a year was Rs.30,000 a month. During the first 5 months, the company saw an average revenue of Rs. 25,000 per month and in the last 6 months, the company saw an average of Rs.33,000 per month. What was the revenue level in the 6th month? Que:
6. 6. 2IIM Ascent Education’s An IIM Alumni Venture Solution The average revenue of company A in a year was Rs.30,000 a month. During the first 5 months, the company saw an average revenue of Rs. 25,000 per month and in the last 6 months, the company saw an average of Rs.33,000 per month. What was the revenue level in the 6th month? Soln: Number * Average = Total 5 25 k 125 k 1 X X 6 33k 198 k 12 30 360 k
7. 7. 2IIM Ascent Education’s An IIM Alumni Venture Solution 125k + x + 198k = 360k x = 37k Company earns Rs. 37k in the sixth month. Soln:
8. 8. 2IIM Ascent Education’s An IIM Alumni Venture Question The captain of a cricket squad of 14 players is 28 years old. The wicket- keeper is 32 years old. If these two players are replaced by two younger players, the average age of the team drops by 1 year. What is the average age of the two new players? Que:
9. 9. 2IIM Ascent Education’s An IIM Alumni Venture Solution The captain of a cricket squad of 14 players is 28 years old. The wicket- keeper is 32 years old. If these two players are replaced by two younger players, the average age of the team drops by 1 year. What is the average age of the two new players? Soln: Number * Average = Total 14 a 14a 2 - 60 12 - 14a – 60 2 X 14a – 60 + 2x 14 a – 1 14(a - 1)
10. 10. 2IIM Ascent Education’s An IIM Alumni Venture Solution 14(a – 1) = 14a - 60 + 2x 14a – 14 = 14a – 60 + 2x 46 = 2x X = 23 Soln:
11. 11. 2IIM Ascent Education’s An IIM Alumni Venture Question The average age of the students of class A comprising 25 students is 19 years and that of the students of class B comprising 15 students is 11 years. What is the average age of the students of the two classes taken together? Que:
12. 12. 2IIM Ascent Education’s An IIM Alumni Venture Solution The average age of the students of class A comprising 25 students is 19 years and that of the students of class B comprising 15 students is 11 years. What is the average age of the students of the two classes taken together? Average age of 25 students = 19 Sum of the ages of 25 students = 25 * 19 = 475 Average age of 15 students = 11 Sum of the ages of 15 students = 15 * 11 = 165 Sum of the ages of 50 students put together = 475 + 165 = 640 Average age of the two classes together = 16 40 640 = Soln:
13. 13. 2IIM Ascent Education’s An IIM Alumni Venture Question The average weight of a class comprising 29 students is 40 kgs. If the weight of the teacher is also included, the average weight increases by 0.5 kgs. What is the weight of the teacher? Que:
14. 14. 2IIM Ascent Education’s An IIM Alumni Venture Solution The average weight of a class comprising 29 students is 40 kgs. If the weight of the teacher is also included, the average weight increases by 0.5 kgs. What is the weight of the teacher? X = 55 kgs Soln: Number * Average = Total 29 40 1160 1 X X 30 40.5 1215
15. 15. 2IIM Ascent Education’s An IIM Alumni Venture Question 30 friends go out for dinner. 12 of them spend Rs.32.5 each for the dinner while the rest of them spend Rs.3 more than the average expense of all 30. What was the total money spent?? Que:
16. 16. 2IIM Ascent Education’s An IIM Alumni Venture Solution 30 friends go out for dinner. 12 of them spend Rs.32.5 each for the dinner while the rest of them spend Rs.3 more than the average expense of all 30. What was the total money spent? 390 + 18(x + 3) = 30x => 390 + 18x + 54 = 30x 440 = 12x => x = 36.67 Soln: Number * Average = Total 12 32.5 390 18 X + 3 18(x + 3) 30 X 30x
17. 17. 2IIM Ascent Education’s An IIM Alumni Venture Question The range of the height of male members in a team is 9 cms, and that of the female members in the team is 8 cms. What is the range of the height of the team if the shortest man in the team is 3 cms taller than the shortest woman in the team? Que:
18. 18. 2IIM Ascent Education’s An IIM Alumni Venture Solution The range of the height of male members in a team is 9 cms, and that of the female members in the team is 8 cms. What is the range of the height of the team if the shortest man in the team is 3 cms taller than the shortest woman in the team? Soln: 9 cm Shortest male Tallest male 8 cm Shortest female Tallest female
19. 19. 2IIM Ascent Education’s An IIM Alumni Venture Solution Soln: 8 cm Shortest female Tallest female Shortest male 3cm Range = 3 + 9 = 12 cm Tallest male
20. 20. 2IIM Ascent Education’s An IIM Alumni Venture Question The median of 68, 93, 109, x, y, and 97 is 97. What is the least possible average of x and y? Que:
21. 21. 2IIM Ascent Education’s An IIM Alumni Venture Solution The median of 68, 93, 109, x, y, and 97 is 97. What is the least possible average of x and y? 68, 93, 97, x, y, 109 Median = 97 Median = Average of 3rd and 4th term. There is already one term than is 97 The only was the median can be 97 is if one of x, y is also 97. So, assuming x =97, the numbers are 68, 93, 97, 109 and y. y has to be greater than or equal to 97. For the least possible average of x and y. y should be 97. Least possible averages = Soln: 97 2 9797 2 yx = + = +