IMPORTANT FORMULAE RELATED TO
AVERAGE OF NUMBERS
1.
Average:
Average =
|
Sum of observations
|
||
Number of
observations
|
2.
Average Speed:
Suppose a man covers a certain distance at x kmph and an equal distance at y kmph.
Then, the average
speed during the whole journey is
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2xy
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kmph.
|
||
x + y
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1.
Average
of first n natural numbers =
(n+1) / 2
2.
Average
of first n Even numbers = (n+1)
3.
Average
of first n odd numbers = n
4.
Average
of consecutive numbers = ( 1st number + Last number) / 2
5.
Average
of 1 to n odd numbers = (Last odd number + 1) / 2
6.
Average
of 1 to n even numbers = (Last even
number + 2) / 2
7.
Average
of squares of 1st n natural numbers = (n+1)(2n+1) / 6
8.
Average
of the cubes of 1st n natural numbers = n(n+1)2 / 4
9.
Average
of n multiplies of any number = Number x (n+1) / 2
PRACTICE PROBLEMS
a. If the weight of A
is 60Kg, weight of B is 45Kg, weight of C is 54kg, then what is the average
weight of three persons ?
b. The average
expenditure of chandan in four days is Rs.90. if his expenditure for the 1st
three are Rs.100, Rs.125 and Rs.85. respectively. Then what is the expenditure
of chandan for the fourth day ?
1. What will be the
average of numbers from 1 to 51 ?
2. Find out the average
of 2, 4, 6, 8, 10, 12, 14.
3. Calculate the
average of 1, 3, 5, 7, 9, 11, 13, 15, & 17
4. What will be the
average of 1, 2, 3, 4, , . . . 51, 52,
53 ?
5. Find out the average
of 4, 7, 10, 13, . . . 28, 31.
6. Find the average of
all the odd numbers and average of all the even numbers from 1 to 45 ?
7. Calculate the average
of the squares of natural numbers from 1 to 25 ?
8. Calculate the
average of the cubes of first 9 natural numbers.
9. what will be the
average of first 9 multiples of 5 ?
PRACTICE SET - 02
1.
Find the average of following set of scores, 253, 124, 255, 534, 836, 375, 101,
443, 760 ?
a. 427 b. 413 c. 141 d. 490
2. Find the average of the following set of scores. 124,
856, 331, 227, 963, 338, 259 & 662.
a. 570 b. 660 c. 141 d.350
3. What will be the average of even numbers between 11 to 63
?
a. 37.5 b.
47 c. 42 d. 37
4. Find the average of all prime numbers between 60 and 90 ?
a. 72 b. 74.7 c. 74 d.
73.6
5. Calculate the average of the cubes of first five natural
numbers.
a. 55 b. 65 c. 45 d. 35
6. Average age of 5 boy is 16 yr. of which that of 4 boys is
16yr 3 months. The age of the 5th boy is ?
a. 15yr b.
15yr 6 months
c. 15yr 4 months d.
15yr 2 months
7. The average of 4 consecutive even numbers is 27. What is
the greatest number ?
a. 28 b. 26 c. 32 d. 30
8. A businessman purchased 30 TV sets in Rs.300000 if the
average cost of 15 TV sets is 9000. Then find out the average cost of remaining
TV sets.
a. 20000 b. 12000 c. 11000 d.
10000
9. The average age of 30 girls is 13 yrs. The average of
first 18yrs girls is 15 yrs. Find out the average age of remaining 12girls.
a. 12yr b.
10yr c. 16yr d. 105yr
10. Find the average of the Following set of numbers
112, 102, 133, &
127
a. 108 b. 118 c. 128 d. 110
11. 746, 348, 1163, 49, 214, 358, 79, 163, Find the average ?
a. 384 b. 396 c. 382 d. 390
12. 125, 133, 298, 345, 446, 507 find average?
a. 309 b. 306 c. 312 d. 315
13. 6 ½, 7 ¼ , 8 ¾, 9 ½ Find average ?
a. 7 b. 8 c. 9 d. 10
14. 246.84, 76.325, 126.5, 8.8, 33.44 average ?
a. 90.125 b.
95.362 c. 98.381 d. 198.89
15. The sum of the marks of 22 students is 1760. Find the
average marks of 45 students ?
a. 2660 b.
2770 c. 2550 d.None
16.The average marks of 24 boys in the class is 70. The
average marks of 16 girls in the class is 60. Then find the average marks of
the class ?
a. 55 b. 66 c. 64 d. 68
17.The average height of 30 boys out of class of 50 boys is
160cm. if the average height of the remaining
boys is 165 cm. the average height of the whole class is ?
a. 162cm b. 163cm c. 164cm d.165cm
18. The average score of a cricketer for10 matches is 38 runs. If the average for the
first six matches is 42. What will be the average of last 4 matches ?
a. 30 b. 31 C. 32 D. 33
19. The average temperature of Monday, Tuesday, &
Wednesday was 400C. the average for Tuesday, Wednesday, and Thursday
was 410C. that for Thursday being 420C. what was the
temperature on Monday ?
a. 350C b. 360C c. 380C d.390C
20. Find the average of first 25 natural numbers ?
21. Find the average of first 84 natural numbers ?
23. Find the average of first 45 even numbers ?
24. Find the average of 1st 124 even numbers ?
25. Find the average of 1st 64 odd numbers ?
26. Find the average of 1st 10 prime numbers ?
27. Find the average of numbers from 144 to 356 ?
28. Find the averge of the numbers from 1111 to 9999 ?
29. Find the average of multiples of 6 lies between 1 and
100 ?
30. Find the average of multiples of 15 lies between 1 and
400 ?
32. Find the average of multiples of 12 lies between 500 and
1500 ?
33. The average of 7 numbers is 65. If the average of 1st
3 numbers is 58, and if the average of last 3 numbers is 68. Find the 4th
number ?
a. 77 b.76 c. 87 d. 86
34. The average of 5 positive numbers is 208. The average of
1st two numbers is 272.5. and the average of last two numbers is
154.5. what is the third number.
a. 168 b. 186 c. 178 d. 187
35. The average of 11 results is 50. If the average of 1st
six results is 48 and the average of last 4 results is 54. Then find the 7th result ?
a. 46 b. 56 c. 66 d.60
36.The average of 5 results is 75. If the average of first 3
results is 72. And the average of last 3 result is 80. Find the 3rd
result ?
a. 31 b. 51 c. 71 d. 81
37. The average expenditure of a mans family during 1st
3 months is 3000/-, next 4 months is 4000/- last five months is 5000/-. And
total savings is 10000/- then find his average family earning ?
a. 7000 b.
8000 c.6000 d.5000
38. the average expenditure of a mans family during 2 months
is 4500/-, next 4 months is 4000/- and last six months is 6500/- and total
savings is 14000/-. Then find his average family earning ?
a. 5500 b.
6500 c. 7500 d.4500
39. The average of 18 numbers is 76. If ‘4’ is subtracted
from each number then what will be the average of the new set of numbers ?
a. 76 b. 72 c. 73 d. 74
40. The average of 15 numbers is 108, if ‘7’ is added to
each number then what will be the average of the new set of numbers ?
a. 101 b. 102 c. 114 d. 115
41. The average of 10 numbers is 18. If each number is
multiplied by ‘8’ then what will be the average of new set of numbers ?
a. 126 b. 144 c. 162 d. 152
42. The average of 24 numbers is 85, if each number is
divided by ‘5’ then what will be the average of new set of numbers ?
a. 16 b. 17 c. 13 d. 14
43. IF 9a + 9b = 1224. What is the average of a & b?
a. 136 b. 138 c. 68 d.
66
44. If 23a + 23b =1656, what is the average of a & b ?
a. 36 b. 40 c. 72 d. 80
45. Of the three numbers. The first number is twice the 2nd
number and 2nd number is thrice the third number. If the average of
these 3 numbers is 20. Then what is the 2nd number ?
a. 6 b. 18 c. 36 d. 48
46. The average age of 5 childrens is 8 years. If the age of
their father is included, then the average age increased by 7 yrs. Find the age
of father ?
a. 45yr b. 47
yr c. 50yr d. 40yr
47. In
the first 10 overs of a cricket game, the run rate was only 3.2. What should be
the run rate in the remaining 40 overs to reach the target of 282 runs?
a. 6.25 b. 6.5 c. 6.75 d. 7
48. In the first 10
overs of a cricket game, the run rate was only 3.2. What should be the run rate
in the remaining 40 overs to reach the target of 282 runs?
a. 28 4/7 Yr b. 31 5/7 Yr c.32 1/7yr
49. A
grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5
consecutive months. How much sale must he have in the sixth month so that he
gets an average sale of Rs. 6500?
a. 4991 b. 5991 c.
6001 d.6991
50. The average of 20 numbers is zero.
Of them, at the most, how many may be greater than zero?
a. 0 b. 1 c. 19 d. 10
51. The
average weight of 8 person's increases by 2.5 kg when a new person comes in
place of one of them weighing 65 kg. What might be the weight of the new
person?
A.76kg b. 76.5 kg c. 85 kg d. data inadequate
52. The
captain of a cricket team of 11 members is 26 years old and the wicket keeper
is 3 years older. If the ages of these two are excluded, the average age of the
remaining players is one year less than the average age of the whole team. What
is the average age of the team?
A. 23yrs b. 24yr c.25yr d.None of these
53. The average monthly
income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs.
6250 and the average monthly income of P and R is Rs. 5200. The monthly income
of P is:
a. 3500 b.
4000 c. 4050 d.
5000
54. The
average age of husband, wife and their child 3 years ago was 27 years and that
of wife and the child 5 years ago was 20 years. The present age of the husband
is:
a. 35yr b.
40yr c. 50yr
d.None of these
55. The average weight
of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B
and C be 43 kg, then the weight of B is:
a. 17kg b. 20 kg c.
26kg d.31kg
56. The average weight
of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg.
Find the average weights of all the boys in the class.
a. 47.55 kg b. 48kg c. 48.55kg d.
49.25kg
57. A pupil's marks were
wrongly entered as 83 instead of 63. Due to that the average marks for the
class got increased by half (1/2). The number of pupils in the class is:
a. 10 b. 20 c. 40 d. 73
58. The average of 100 observations was calculated as 35. It
was found later on that one of the observations was misread as 24 instead of 42
then find the correct average
a. 35.18 b. 34.92 c.36.29 d.40.1
59.the average of 100 observations was calculated as 48. It
was found later on that one of the observations was misread as 37 instead of
73. Then find the correct average ?
a. 47.74 b.42.74 c.48.36 d.43.74
60. The average of 10 observations was calculated as 65. It
was later found that one of the observations was misread as 72. Instead of 27.
Find the correct average.
a. 64.55 b.60.50 c.64.50 d.69.50
61. the average of 5 consequent numbers is 64. Find the
first number.
a.26 b.62 c.73 d.37
62. The average of 7 consequent numbers is 107. Find the
last number ?
a. 110 b.120 c.130 d.140
63. The average of 6 consecutive even numbers.
A,B,C,D,E,&F is 47. What is the product of C&F ?
a. 1392 b.2392 c.3392 d.1892
64. The average of 5 consecutive odd numbers. A,B,C,D,E is
83. What is the sum of A & E ?
a.661 b.616 c. 166 d. 81
65. The average of 4 consecutive odd numbers. A,B,C,D is 36.
What is the product of A & C ?
a. 2112 b.1122 c. 2211 d.1221
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