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Average

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Q 1. A student was asked to find the arithmetic mean of the following 12 numbers :

{tex} 3, 11, 7,9,15,13,8,19,17, 21, 14{/tex} and {tex} \mathrm x {/tex}

He found the mean to be {tex} 12 . {/tex} The value of {tex} \mathrm { x } {/tex} will be:

3

7

17

31

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Q 2. The average of the marks obtained in an examination by 8 students was 51 and by 9 other students was {tex} 68 . {/tex} The average marks of all 17 students was :

59

59.5

60

60.5

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Q 3. If the average marks of three batches of 55,60 and 45 students respectively is 50,55 and 60, then the average marks of all the students is

54.68

53.33

55

None of these

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Q 4. The average of 30 results is 20 and the average of other 20 results is 30 . What is the average of all the results?

24

48

25

50

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Q 5. If the average weight of 6 students is {tex} 50 \mathrm { kg } {/tex}; that of 2 students is {tex} 51 \mathrm { kg } {/tex}; and that of other 2 students is {tex} 55 \mathrm { kg } {/tex}; then the average weight of all students is

{tex} 61\ \mathrm { kg } {/tex}

{tex} 51.5\ \mathrm { kg } {/tex}

{tex} 52\ \mathrm { kg } {/tex}

{tex} 51.2\ \mathrm { kg } {/tex}

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Q 6. The average of 10 numbers is 7. If each number is multiplied by {tex} 12 , {/tex} then the average of the new set of numbers will be

7

19

82

84

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Q 7. The average income of 40 persons is Rs. 4200 and that of another 35 persons is Rs. 4000. The average income of the whole group is :

Rs. 4100

Rs. {tex} 4106 \frac { 1 } { 3 } {/tex}

Rs. {tex} 4106 \frac { 2 } { 3 } {/tex}

Rs. {tex} 4108 \frac { 1 } { 3 } {/tex}

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Q 8. The average weight of five persons sitting in a boat is {tex} 38 \mathrm { kg } {/tex}. The average weight of the boat and the persons sitting in the boat is {tex} 52 \mathrm { kg } {/tex}. What is the weight of the boat?

{tex} 228 \mathrm { kg } {/tex}

{tex} 122 \mathrm { kg } {/tex}

{tex} 232 \mathrm { kg } {/tex}

{tex} 242 \mathrm { kg } {/tex}

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Q 9. The average marks of 32 boys of section A of class {tex} X {/tex} is 60 whereas the average marks of 40 boys of section {tex} B {/tex} of class {tex} X {/tex} is {tex} 33 . {/tex} The average marks for both the sections combined together is

44

45

{tex} 46 \frac { 1 } { 2 } {/tex}

{tex} 45 \frac { 1 } { 2 } {/tex}

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Q 10. Total weekly emoluments of the workers of a factory is Rs {tex} 1534 . {/tex} Average weekly emolument of a worker is Rs {tex} 118 {/tex}. The number of a workers in the factory is :

16

14

13

12

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Q 11. 12 kg of rice costing Rs. 30 per kg is mixed with 8 kg of rice costing Rs. 40 per kg. The average per kg price of mixed rice is

Rs. 38

Rs. 37

Rs. 35

Rs. 34

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Q 12. If average of 20 observations {tex} x _ { 1 } {/tex}, {tex} x _ { 2 } , \ldots . , x _ { 20 } {/tex} is {tex} y , {/tex} then the average of {tex} x _ { 1 } - 101 , x _ { 2 } - 101 , x _ { 3 } - {/tex} {tex} 101 , \ldots . . , x _ { 20 } - 101 {/tex} is

{tex} y - 20 {/tex}

{tex} y - 101 {/tex}

{tex} 20 y {/tex}

{tex} 101 y {/tex}

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Q 13. The average of {tex} x {/tex} numbers is {tex} y {/tex} and average of {tex} y {/tex} numbers is {tex} x {/tex}. Then the average of all the numbers taken together is

{tex} \frac { x + y } { 2 x y } {/tex}

{tex} \frac { 2 x y } { x + y } {/tex}

{tex} \frac { x ^ { 2 } + y ^ { 2 } } { x + y } {/tex}

{tex} \frac { x y } { x + y } {/tex}

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Q 14. The average of {tex} x {/tex} numbers is {tex} y ^ { 2 } {/tex} and the average of {tex} y {/tex} numbers is {tex} x ^ { 2 } . {/tex} So the average of all the numbers taken together is

{tex} \frac { x ^ { 3 } + y ^ { 3 } } { x + y } {/tex}

{tex} x y {/tex}

{tex} \frac { x ^ { 2 } + y ^ { 2 } } { x + y } {/tex}

{tex} x y ^ { 2 } + y x ^ { 2 } {/tex}

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Q 15. The average of {tex} n {/tex} numbers {tex} x _ { 1 } , x _ { 2 } , {/tex} {tex} \ldots x _ { n } {/tex} is {tex} \bar { x } {/tex}. Then the value of {tex}\displaystyle \sum _ { i = 1 } ^ { n } \left( x _ { i } - \bar { x } \right) {/tex} is equal to

{tex} n {/tex}

0

{tex} n \bar { x } {/tex}

{tex} \bar { x } {/tex}

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Q 16. A man bought 13 articles at {tex} Rs. 70 {/tex} each, 15 at {tex} Rs. 60 {/tex} each and 12 at {tex} Rs. 65 {/tex} each. The average price per article is

Rs. 60.25

Rs. 64.75

Rs. 65.75

Rs. 62.25

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Q 17. A library has an average number of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with Sunday is:

285

295

300

290

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Q 18. The average of 30 numbers is 40 and that of other 40 numbers is 30. The average of all the numbers is

{tex} 34 \frac { 2 } { 7 } {/tex}

35

34

34.5

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Q 19. The average of 20 numbers is 15 and the average of first five is {tex} 12 . {/tex} The average of the rest is

16

15

14

13

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Q 20. The average monthly expenditure of a family is {tex} Rs. 2,200 {/tex} during first three months, {tex} Rs. 2,550 {/tex} during next four months and {tex} Rs. 3,120 {/tex} during last five months of the year. If the total savings during the year was {tex} Rs. 1,260 , {/tex} what is the average monthly income?

{tex} Rs. 1,260 {/tex}

{tex} Rs. 1,280 {/tex}

{tex}Rs. 2,805 {/tex}

{tex}Rs. 2,850{/tex}

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Q 21. Find the average of {tex} 1.11,0.01 , {/tex} {tex} 0.101,0.001,0.11 {/tex}

0.2664

0.2554

0.1264

0.1164

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Q 22. 4 boys and 3 girls spent Rs. 120 on the average, of which boys spent Rs. 150 on the average. Then the average amount spent by the girls is

Rs. 80

Rs. 60

Rs. 90

Rs. 100

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Q 23. Six tables and twelve chairs were bought for {tex} Rs. 7,800 {/tex}. If the average price of a table is {tex} Rs. 750 , {/tex} then the average price of a chair would be

Rs. 250

Rs. 275

Rs. 150

Rs. 175

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Q 24. Out of 20 boys, 6 are each of {tex}1\ \mathrm { m }\ 15\ \mathrm { cm } {/tex} height, 8 are of {tex}1\ \mathrm { m }\ 10\ \mathrm { cm } {/tex} and rest of {tex}1\ \mathrm { m }\ 12\ \mathrm { cm } {/tex}. The average height of all of them is

{tex} 1\ \mathrm { m }\ 12.1\ \mathrm { cm } {/tex}

{tex} 1\ \mathrm { m }\ 21.1\ \mathrm { cm } {/tex}

{tex} 1\ \mathrm { m }\ 21\ \mathrm { cm } {/tex}

{tex} 1\ \mathrm { m }\ 12\ \mathrm { cm } {/tex}

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Q 25. There are two groups A and B of a class, consisting of 42 and 28 students respectively. If the average weight of group A is {tex} 25 \mathrm { kg } {/tex} and that of group {tex} \mathrm { B } {/tex} is {tex} 40 \mathrm { kg } {/tex}, find the average weight of the whole class.

{tex} 69\ \mathrm { kg } {/tex}

{tex} 31\ \mathrm { kg } {/tex}

{tex} 70\ \mathrm { kg } {/tex}

{tex} 30\ \mathrm { kg } {/tex}

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