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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
The mean of 8 numbers is 25. if 5 is subtracted from each number, what will be the new mean ? |
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Answer» Let the given numbers be ` ,x_(1),x_(2),…,x_(3)` Then, the mean of these numbers = `((x_(1) +x_(2) +….+x_(3))/8` `(x_(1)+x_(2)+....+x_(3))/8=25Rightarrow(x_(1)+x_(2)+....+x_(8))=200` The new numbers are `(x_(1) -5) ,(x_(2) -5) ,…..,(x_(8)-5)` The new numbers are `((x_(1) -5) +(x_(2)-5) +......+(x_(8)-5))/ 8` `((x_(1)+x_(2)+....+x_(3))-40)/8=(200-40)/8` = ` 160/8 =20` Hence, the new mean is 20. |
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| 52. |
The mean of 12 numbers is 40. if each number is divided by 8, what will be the mean of the new numbers ? |
| Answer» Correct Answer - 5 | |
| 53. |
The mean of 24 numbers is 35. if 3 is added to each number, what will be the new mean ? |
| Answer» Correct Answer - 38 | |
| 54. |
The mean of 15 numbers is 27. if each number is multiplied by 4, what will be the mean of the new numbers ? |
| Answer» Correct Answer - 108 | |
| 55. |
The mean of 20 numbers is 43. if 6 is subtracted from each of the numbes what will be the new mean ? |
| Answer» Correct Answer - 37 | |
| 56. |
Find the median of 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22. |
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Answer» By arranging the numbers in ascending order We get 6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25 We know that n = 11 is odd So we get Median = ½ (n + 1) th term By substituting the values Median = ½ (11 + 1) th term It can be written as Median = value of the 6th term = 16 We get Median = 16 |
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| 57. |
Find the median of 15, 6, 16, 8, 22, 21, 9, 18, 25. |
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Answer» By arranging the numbers in ascending order We get 6, 8, 9, 15, 16, 18, 21, 22, 25 We know that n = 9 is odd So we get Median = ½ (n + 1) th term By substituting the values Median = ½ (9 + 1) th term It can be written as Median = value of the 5th term = 16 We get Median = 16 |
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| 58. |
Find the median of 9, 25, 18, 15, 6, 16, 8, 22, 21. |
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Answer» The value of the middle-most observation is called the median of the data. First arrange the given numbers in ascending order, 6, 8, 9, 15, 16, 18, 21, 22, 25 Here n = 9, which is odd. Where, n is the number of the given number. ∴median = value of ½ (n + 1)th observation. = ½ (9 + 1) = ½ (10) = 10/2 = 5 Then, value of 5th term = 16 Hence, the median is 16. |
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| 59. |
Find the median of 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22. |
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Answer» The value of the middle-most observation is called the median of the data. First arrange the given numbers in ascending order, 6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25 Here n = 11, which is odd. Where, n is the number of the given number. ∴median = value of ½ (n + 1)th observation. = ½ (11 + 1) = ½ (12) = 12/2 = 6 Then, value of 6th term = 16 Hence, the median is 16. |
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| 60. |
The mean of 20 numbers is 18. if 3 is added to each of the first ten numbers, find the mean of the new set of 20 numbers. |
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Answer» Correct Answer - 19.5 New mean =` ((20 xx 18) + ( 3 xx10))/20 = 390/20 = 39/2 = 19.5 ` |
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| 61. |
The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean? |
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Answer» Let the given numbers be `x_(1),x_(2),x_(3),…., x_(16)` Then , the mean of these numbers = `( x_(1) +x_(2)+x_(3) +….+x_(16))/16` `( x_(1) +x_(2)+x_(3) +….+x_(16))/16 =8 ` `Rightarrow (x_(1) +x_(2)+x_(3) +….+x_(16)) =128` The new numbers are `(x_(1) +2) ,(x_(2) +2),(x_(3)+2) ,.....,(x_(16) +2)` mean of the new numbers `((x_(1)+2)+(x_(2)+2)+(x_(3)+2)+.....+(x_(16)))/16` `((x_(1)+x_(2)+x_(3)+....+x_(16))+32)/16=((128+32))/16` `160/16 = 10` Hence, the new mean is 10. |
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| 62. |
The mean of 150 items was found to be 60. Later on, it was discovered that the values of two items were misread are 52 and 8 instead of 152 and 88 respectively. Find the correct mean. |
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Answer» It is given that Mean of 150 items = 60 So the total sum = 150 (60) = 9000 We know that Correct sum of items = sum of 150 items – sum of wrong items + sum of right items By substituting the values Correct sum of items = 90000 – (52 + 8) + (152 + 88) On further calculation Correct sum of items = 9000 – 60 + 240 So we get Correct sum of items = 9180 So the correct mean = correct sum of items/ total number of items By substituting the values Correct mean = 9180/150 = 61.2 Therefore, the correct mean is 61.2. |
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| 63. |
The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result. |
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Answer» It is given that Mean of 31 results = 60 So the total sum = 31 (60) = 1860 We know that Mean of first 16 results = 58 So the total sum = 16 (58) = 928 Mean of last 16 results = 62 So the total sum = 16 (62) = 992 We get the 16th result = total sum of first 16 results + total sum of last 16 results – total sum of 31 results By substituting the values 16th result = 928 + 992 – 1860 On further calculation 16th result = 1920 – 1860 = 60 Therefore, the 16th result is 60. |
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| 64. |
The mean of the marks scored by 50 students was found to be 39 later on, it was observed that a score was 43 was misread as 23 find the correct mean.A. 38.6B. 39.4C. 39.8D. 39.2 |
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Answer» Correct Answer - b calculated sum =` ( 39 xx 50) = 1950` correct sum = ( 1950 +43-23) =1970 Correct mean = `1970/50 = 39.4` |
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| 65. |
The runs scored by 11 members of a cricket team are 15,29,43,13,31,50,20,0,27,56,34 find the median score. |
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Answer» Arrranging the runs in an ascending order, we have 0,13,15,20,27,29,31,34,43,50,56 Here ,n=11, which is odd. Median sorce = value of `((11+1)/2)` th term = value of 6th term =29 Hence, the median score is 29. |
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| 66. |
The median of the numbers 84,78,54,56,68,22,34,45,39,54 isA. 45B. 49.5C. 54D. 56 |
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Answer» Correct Answer - c The given numbers in an asscending order are 22,34,39,45,54,54,56,78,84. Here n=10 which is even. median = `1/2` [5th term + 6th item] = ` 1/2 (54 +54) =54` |
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| 67. |
If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations. |
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Answer» We know that Number of observations = 5 It is given that mean = 13 We can write it as [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]/5 = 13 On further calculation 5x + 20 = 13 (5) So we get 5x + 20 = 65 By subtraction 5x = 45 By division x = 9 By substituting the value of x We know that the last three observations are 9 + 4 = 13 9 + 6 = 15 9 + 8 = 17 We know that Mean of last three observations = (13 + 15 + 17)/3 On further calculation Mean of last three observations = 45/3 By division Mean of last three observations = 15 Therefore, the mean of last three observations is 15. |
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| 68. |
The numbers 50, 42, 35, (2x + 10), (2x – 8), 12, 11, 8 have been written in a descending order. If their median is 25, find the value of x. |
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Answer» We know that n = 8 which is even It is given that median = 25 We can write it as ½ {(n/2)th term + (n/2 + 1)th term} = 25 By substituting the values ½ {(8/2)th term + (8/2 + 1)th term} = 25 So we get ½ {4th value + 5th value} = 25 It can be written as (2x + 10 + 2x – 8)/2 = 25 On further calculation 4x + 2 = 50 By subtraction 4x = 48 By division x = 12 Therefore, the value of x is 12. |
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| 69. |
Find the mean of first five natural numbers. |
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Answer» The first five natural number are 1, 2, 3, 4 and 5. ∴mean = (sum of the given numbers)/ (number of the given numbers) Then, Sum of the five natural numbers, = 1 + 2 + 3 + 4 + 5 = 15 Number of the given number = 5 Now, mean = 15 / 5 = 3 Hence, the mean of the five natural numbers is 3. |
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| 70. |
Write the data given below in ascending order and prepare the frequency table.7, 8, 7, 10, 6, 8, 9, 7, 10, 5, 7, 6, 8, 5, 6, 7, 8, 9, 7, 6, 7, 8 |
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Answer» Arranging the data in ascending order, we get 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10
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| 71. |
Fill in the blanks:Arranging the numerical figures in ascending or descending order is called an …….. |
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Answer» Array According to the definition, arranging the numerical figures of a data in ascending or descending order is called an array. |
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| 72. |
Fill in the blanks:Data means information in the form of …… figures. |
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Answer» Numerical According to the definition, a collection of numerical figures giving some particular type of information is called data. |
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| 73. |
Fill in the blanks:Arranging the data in the form of a table is called ……… of data. |
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Answer» Tabulation According to the definition, arranging the data in a systematic form in the form of a table is called tabulation of data. |
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| 74. |
Fill in the blanks:Data obtained in the ……… form is called raw data. |
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Answer» Original According to the definition, Data obtained in the original form is called raw data. |
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| 75. |
Define the terms:(i) Data(ii) Raw data(iii) Array(iv) Tabulation of data(v) Observation(vi) Frequency of an observation(vii) Statistics |
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Answer» (i) Data A collection of numerical figures giving some particular type of information is called data. (ii) Raw data Data obtained in the original form is called raw data. (iii) Array Arranging the numerical figures of a data in ascending or descending order is called an array. (iv) Tabulation of data Arranging the data in a systematic form in the form of a table is called tabulation of data. (v) Observation Each numerical figure in a data is called an observation. (vi) Frequency of an observation The number of times a particular observation occurs is called its frequency. (vii) Statistics It is the subject that deals with the collection, presentation, analysis and interpretation of numerical data. |
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| 76. |
In a classthere are 50 students. Their average weight is 45 kg. When a student leavesthe class, the average is reduced by 100 g. Find the weight of the studentwho left the class. |
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Answer» Correct Answer - 48 kg Total weight of 36 students = `( 41 xx 36) ` kg = 1476 kg New mean = ( 41-0.2) kg = 40 .8 kg Total weight of 35 students = ` ( 40.8 xx 35)` kg = 1428 kg |
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| 77. |
The mean of 8 numbers is 35. if a number is excluded then the mean is reduced by 3. find the excluded number. |
| Answer» Correct Answer - 56 | |
| 78. |
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is |
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Answer» Mean of the given five numbers= 30 Sum of these five numbers ` = ( 30xx 5) = 150` mean of the remaining four numbers = 28 Sum of these numbers =` ( 28xx 4) =112` Excluded number = ( 150 -112) =38. |
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| 79. |
Find the missing frequency p for the following frequency distributions whose mean is 28.25. |
| Answer» Correct Answer - p=10 | |
| 80. |
Find the missing frequencies in the following frequency distribution whose mean is 34. |
| Answer» Correct Answer - `f_(i) =6, f_(2)=10` | |
| 81. |
The mean of the following distribution is 50. Find the value of a and hence the frequencies of 30 and 70. |
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Answer» Correct Answer - a=5, `f_(30)=28,f_(70) =24` ` (170+30(5a+3) +1600 +70 (7a -11) +1710)/(60 +12a) =50` ` Rightarrow = 64a +2800 = 3000 +600a Rightarrow 40a = 200 Rightarrow a=5` |
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| 82. |
if `overlinex` is the mean of `x_(1),x_(2),x_(3),….,x_(n) " then "sum_(n)^(i=1) (x_(i) -overlinex)=?` |
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Answer» Correct Answer - b `overset(n)underset(i=1) sum (x_(i) -overlinex)= (x_(1) - overlinex) +(x_(2) -overlinex) +….+(x_(n) -overlinex)` `= ( x_(1)+x_(2) +…..+ x_(n))-noverlinex= (noverlinex - noverlinex)=0` |
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| 83. |
If the mean of the observation x, x+3, x+5, x+7 and x+10 is 9, then mean of the last three observations isA. `10""1/3`B. `10""1/2`C. `11""1/3`D. `11""2/3` |
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Answer» Correct Answer - c `(x+x+3+x+5+x+x+7+x+10)/5= 9 Rightarrow 5x +25 =45 Rightarrow 5x =20 Rightarrow 20 Rightarrow x=4` Last 3 observations are 9,11,14 Their mean `= (9+11+14)/3= 34/3 = 11""1/3` |
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| 84. |
If the mean of the observation x, x+3, x+5, x+7 and x+10 is 9, then mean of the last three observations is |
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Answer» Mean of the given five observations ` (x +(x+3) +(x+5) +(x+10))/5` ` = ((5x +25))/5= (5(x+5))/5 = (x +5)` But, mean of these observations is 9 (given) But , mean of these observations is 9 (given) ` x+5=9 Rightarrow x=3-5=4` So the last three observations are (4+5),(4+7),(4+10) i.e, 9,11,14. Mean of these observations= `((9+ 11+14))/3 = 34/3 = 11""1/3` |
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| 85. |
The mean of 25 observation is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is |
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Answer» Mean of 25 observations =` (36xx 25) =900` Sum of 25 observations = `(36 xx 25) =900` Mean of first 13 observations =32. Sum of first 13 observations `= (32 xx 13) = 416` Mean of last 13 observations = 40 Sum of last 13 observations =` ( 40xx 13) = 520` 13th observation = ( sum of first 13 observations) + ( sum of last 13 observations) - ( sum of 25 observations ) = ( 416 + 520) -(900) = 936 -900 = 36 |
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| 86. |
If each observation of the data is decreased by 8 then their meanA. remains the sameB. is decreased by 8C. is increased by 5D. becomes 8 times the original mean |
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Answer» Correct Answer - b If each observation is decresed by 8 then the mean is decreased by 8. |
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| 87. |
The mean of 100 observation is 50. If one of the observation which was 50 is replaced by 150, the resulting mean will beA. 50.5B. 51C. 51.5D. 52 |
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Answer» Correct Answer - b Resulting sum = `( 50 xx 100 -50 +150) =( 5150 -50) = 5100` Resultingh mean = `5100/100 = 51` |
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| 88. |
The average weight of 10 oarsmen in a boat is increased by 1.5kg when one of the crew who weighs 58kg is replaced by a new man. Find the weight of the new man. |
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Answer» It is given that Weight of 10 oarsmen is increased by 1.5kg So the total weight increased = 1.5 (10) = 15kg It is given that one of the crew who weights 58kg is replaced by a new man So we get the weight of new man = weight of man replaced + total weight increased By substituting the values Weight of the new man = 58 + 15 = 73kg Therefore, the weight of a new man is 73kg. |
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| 89. |
The average weight of 15 oarsmen in a boat is increased by 1.6 kg when one of the crew, who weighs 42 kg is replaced by a new man. Find the weight of the new man (in kg). |
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Answer» Correct Answer - 73 kg Total weight increased = `( 1.5 xx 10) ` kg = 15kg weight of the new man = ( 58 + 15) kg = 73 kg |
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| 90. |
Calculate the mode of the following sizes of shoes sold by a shop on a particular day. 5,9,8,6,9,4,3,9,1,6,3,9,7,1,2,5,9 |
| Answer» Correct Answer - 9 | |
| 91. |
A ship sails out an island at the rate of 15km/hr and sails back to the starting point at 10km/hr . Find the average sailing speed an average speed for the whole journey. |
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Answer» Correct Answer - 12 km/hr Let the distance of one side journey be x km. then , total time taken = `( x/15 + x/10) hr = ((5x)/30) hr = (x/6)` hr. Average speed for the whole journey = `{ (2x)/((x//6))}` km/hr = 12 km/hr . |
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| 92. |
The number of children in 10 families of a locality are 2,4,3,4,2,0,3,5,1,6.Find the mean number of children per family. |
| Answer» Correct Answer - 3 | |
| 93. |
The aggregate monthly expenditure of family was ₹18720 during the first 3 months. ₹20340 during the next 4 months and ₹21708 during the last 5 months of year. If the total savings during the year be ₹35340 find the average monthly income of the family. |
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Answer» Correct Answer - ₹ 23450 Total yearly income `= ₹ ( 18720 xx 3+20340 xx4 + 21708 xx 5 + 35340)` ` = ₹ ( 56160 + 81360 +108540 + 35340) = ₹ 281400` |
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| 94. |
The mean monthlysalary paid to 75 workers in a factory is Rs 5680. The mean salary of 25 ofthem is Rs 5400 and that of 30 others is Rs 5700. The mean salary of theremaining workers is(a) Rs5000 (b) Rs 6000 (c) Rs 7000 (d) Rs 8000 |
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Answer» Correct Answer - ₹ 6000 Total weekly payment to remaining 20 workers. `= ₹ [ ( 5680 xx 75) - (5400 xx 25 + 5700 xx 30)]` |
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| 95. |
The daily minimum temperature recorded ( in `.^(@)F` ) at a place during six days of a week was as under : find the mean temperature . |
| Answer» Correct Answer - `29.9^(@)F` | |
| 96. |
Find the mean of daily wages of 40 workers in a factory as per data given below: |
| Answer» Correct Answer - ₹ 341.25 | |
| 97. |
batsman in his 12 th inning makes a score of 63 runs and thereby increases his average score by 2. His average after the 12 th inning will be : (a) `65` (b) `39` (c) `41` (d) `53` |
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Answer» Let the average score of 12 innings be x. Then , the average score of 11 innings = (x -2) Total score of 12 innings = 12x. Total score of 11 innings = 11 (x-2) = (11x -22) Score of the 12th innings = ( total score of 12 innings)- ( totl score of 11 innings ) = [12x -(11 x-22)] = (x+22) x +22 = 63 ` Rightarrow` x =41 Hence, the average score after the 12th innings is 41. |
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| 98. |
Find the mean of the first six multiples of 3. |
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Answer» The first six multiples of 3 are 3,6,9,12,15 and 18 Their mean = `(( 3+6+9+12+15+18))/6 = 63/6 = 10""1/2` |
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| 99. |
Find the mean of first eight prime numbers. |
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Answer» The first eight prime numbers are 2,3,5,7,11,13,17,19 their mean = `(( 2+3+5+7+11+13+17+19))/8` ` = 77/8 = 9""5/8` |
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| 100. |
If the mean of 5 observation x, x + 2, x + 4, x + 6 and x + 8 find the value of x |
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Answer» Mean of given observations = \(\cfrac{sum \,of \,given \,observation}{total \,number \,of \,observation}\) ∴ 11 = \(\cfrac{x +(x+2)+(x+4)+(x+6)+(x+8)}{5}\) ⇒ 55 = 5x + 20 ⇒ 5x = 55 – 20 ⇒ 5x = 35 ⇒ x = 35/5 ⇒ x = 7 Hence, the value of x is 7. |
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