AVERAGE

Definition: Average (A) is the ration between sum (S) of the quantities and the number (N) of quantities.

E.g. 1: Find the average of the following set of scores.124, 856, 331, 227, 963, 338, 259 and 662a) 570 b) 660 c) 480d) 350 e) None of these ANSWER: eN = 8 , S = (124 + 856 + 331 + 227 + 963 + 338 + 259 + 662) = 3760

E.g. 2: If 47a + 47b = 5452, what is the average of a and b?a) 116 b) 235 c) 96 d) 58 e) None of these ANSWER: dAverage (A) of a and b = 47a + 47b = 5452 Þ (a + b) =

E.g. 3: The average of four positive integers is 73.5. The highest integer is 108 and the lowest integer is 29. The difference between the remaining two integers is 15. Which of the following is the smaller of the remaining two integers?a) 80 b) 86 c) 73 d) Cannot be determinede) None of these ANSWER: eLet a, b, c and d be the four integers in descending orderThen a + b + c + d = 73.5 × 4 = 294a = 108 d = 29a + d = 137b + c = 294 - 137 = 157Also b - c = 15

CONCEPT 1: The average of n-consecutive even integers or n-consecutive odd integers is equal to the middle number if n is odd.

E.g. 4: The average of 5 consecutive even numbers A, B, C, D and E respectively is 74. What is the product of C and E?a) 5928 b) 5616 c) 5538 d) 5772 e) None of these ANSWER: dA, B, C, D and E are 5-consecutive even integers.

Therefore their average = middle value = CC = 74 D = 74 + 2 = 76 E = 76 + 2 = 78C × E = 74 × 78 = 5772

E.g. 5: The average of 7 consecutive odd numbers is 77. What is the difference between the squares of the greatest and the smallest numbers?a) 5893 b) 5983 c) 5993d) 6241 e) None of these ANSWER: eA, B, C, D, E, F and G be the consecutive odd numbers then their average = D = 77G = D + 6 = 83A = D - 6 = 71G2 - A2 = 832 - 712 = 1848CONCEPT 2: The average of n-consecutive even numbers or n-consecutive odd numbers is equal to the average of middle two numbers if n is even. In the above case if the average is x the middle two numbers will be (x - 1) and (x + 1) respectively.

E.g. 6: The average of 4 consecutive odd numbers A, B, C and D is 62. What is the product of B and D?a) 3695 b) 3965 c) 3569d) 3595 e) None of these ANSWER: bThe average of A, B, C and D is equal to the average of B and C which is 62.B = 62 - 1 = 61C = 62 + 1 = 63 D = 65B × D = 61 × 65 = 3965

E.g. 7: The average of 6 consecutive even numbers A, B, C, D, E and F is 87. What is the value of (10E - 9A)?a) 126 b) 156 c) 172d) 152 e) None of these ANSWER: eAverage of the numbers is equal to the average of middle two numbers C and D. C = 87 - 1 = 86 D = 87 + 1 = 88E = D + 2 = 90A = C - 4 = 86 - 4 = 8210E - 9A = 10 × 90 - 9 × 82 = 900 - 738 = 162CONCEPT 3: The average of a group of n-quantities is A. If one more quantity whose value is x is added to the group such that the average increases by 'i' then x = A + i × (n + 1)

Note: In the above case if there is a reduction in the average then take 'i' as negative.

E.g. 8: The average age of a group of 32 boys is 19 years. If the teacher's age is included the average age of the boys and the teacher becomes 20 years. What is class teacher's age?a) 46 years b) 50 yearsc) 54 years d) 52 yearse) None of these ANSWER: dn = 32 A = 19i = 20 - 19 = 1 x =?x = A + i × (n + 1) = 19 + 1 (32 + 1) 19 + 33 = 52 years

PRACTICE BITS1. If a, b, c, d, e are five consecutive odd integers, and then what is the average?a) a + 4 b) abcde/5 c) 5(a + b + c + d + e)d) a + 8 e) None of these

2. The average salary of 20 workers in an office is Rs 1900 per month. If the manager's salary is added, the average becomes Rs 2000 per month. The manager's annual salary (in Rs) is:a) 24000 b) 25200c) 45600d) Can't be determinede) None of these

3. The average of 6 numbers is 8. What is the 7th number so that the average becomes 10?a) 22 b) 18 c) 21 d) 20e) None of these

4. The average age of 30 students and the class teacher is 20 years. If the class teacher's age is excluded, the average reduces by 1 year. What is the age of the class teacher?a) 39 years b) 50 yearsc) 40 years d) 49 yearse) None of these

5. The average of a set of 5 consecutive even numbers is 88. What is the average of the set of next five even numbers?a) 90 b) 92 c) 100d) 96 e) None of these

6. The average age of 10 persons in a committee is increased by 1 year when two men aged 42 years and 38 years are substituted by two women. Find the average age of these two women?a) 46 years b) 45 yearsc) 42 years d) 44 years e) None of these

7. In a class there are 24 boys whose average age is decreased by 3 months, when 1 boy aged 20 years is replaced by a new boy. Find the age of the new boy?a) 14 years b) 16 yearsc) 17 years d) 18 yearse) None of these

8. Mean of 100 observations is 45. It was later found that two observations is 19 and 31 were incorrectly recorded as 91 and 13. The correct mean is?a) 44.00 b) 44.46 c) 45.00d) 45.54 e) None of these

Answers1 a 2 e 3 a 4 b 5 e 6 b 7 a 8 b