Average
- The average of x numbers is y2 and the average of y numbers is x2. So the average of all the numbers taken together is
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Total sum of x numbers = xy2
Total sum of y numbers = yx2∴ Required average = xy2 + yx2 x + y ∴ Required average = xy(y + x) = xy x + y
Second method to find the required average ,
Here, n1 = x, a1 = y2
n2 = y, a2 = x2∴ Average = n1a1 + n2a2 n1 + n2
Correct Option: B
Total sum of x numbers = xy2
Total sum of y numbers = yx2∴ Required average = xy2 + yx2 x + y ∴ Required average = xy(y + x) = xy x + y
Second method to find the required average ,
Here, n1 = x, a1 = y2
n2 = y, a2 = x2∴ Average = n1a1 + n2a2 n1 + n2 Average = xy2 + yx2 x + y Average = xy 
x + y 
= xy x + y
- If average of 20 observations x1, x2, ....., x20 is y, then the average of x1 – 101, x2 – 101, x3 – 101, ....., x20 –101 is
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Given Here , average of 20 observations x1, x2, ....., x20 = y
Now , we haveRequired average = { ( x1 - 101 ) + ( x2 - 101 ) + . . . . + ( x20 - 101 ) } 20 Required average = { x1 + x2 + . . . . +x20 } - { 101 × 20 } 20
Correct Option: B
Given Here , average of 20 observations x1, x2, ....., x20 = y
Now , we haveRequired average = { ( x1 - 101 ) + ( x2 - 101 ) + . . . . + ( x20 - 101 ) } 20 Required average = { x1 + x2 + . . . . +x20 } - { 101 × 20 } 20 Required average = x1 + x2 + . . . . +x20 - 101 × 20 20 20
Hence , Required average = y - 101
- Total weekly emoluments of the workers of a factory is ₹ 1534. Average weekly emolument of a worker is ₹ 118. The number of workers in the factory is :
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Here , Average weekly emolument of a worker = ₹ 118
Total weekly emoluments of the workers = ₹ 1534
As we know that ,Number of workers in the factory = Total weekly emoluments of the workers Average weekly emolument of a worker
Correct Option: C
Here , Average weekly emolument of a worker = ₹ 118
Total weekly emoluments of the workers = ₹ 1534
As we know that ,Number of workers in the factory = Total weekly emoluments of the workers Average weekly emolument of a worker Number of workers in the factory = 1534 = 13 118
- The average of 30 results is 20 and the average of other 20 results is 30. What is the average of all the results ?
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Here, n1 = 30, a1 = 20
n2 = 20, a2 = 30
We know that ,∴ Required average = n1a1 + n2a2 n1 + n2 Required average = 20 × 30 + 20 × 30 30 + 20
Correct Option: A
Here, n1 = 30, a1 = 20
n2 = 20, a2 = 30
We know that ,∴ Required average = n1a1 + n2a2 n1 + n2 Required average = 20 × 30 + 20 × 30 30 + 20 Required average = 600 + 600 50 Required average = 1200 = 24 50
- The average of the marks obtained in an examination by 8 students was 51 and by 9 other students was 68. The average marks of all 17 students was :
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The average of the marks obtained in an examination by 8 students = 51
Sum of total number of 8 students in exam = 8 × 51 = 408
The average of the marks obtained in an examination by 9 other students = 51
Sum of total number of 9 students in exam = 9 × 68 = 612∴ Required average = 408 + 612 17 Required average = 1020 = 60 17
Second method to find the required average ,
Here, n1 = 8, a1 = 51
n2 = 9, a2 = 68∴ Average = n1 + n2
Correct Option: C
The average of the marks obtained in an examination by 8 students = 51
Sum of total number of 8 students in exam = 8 × 51 = 408
The average of the marks obtained in an examination by 9 other students = 51
Sum of total number of 9 students in exam = 9 × 68 = 612∴ Required average = 408 + 612 17 Required average = 1020 = 60 17
Second method to find the required average ,
Here, n1 = 8, a1 = 51
n2 = 9, a2 = 68∴ Average = n1a1 + n2a2 n1 + n2 Average = 8 × 51 + 9 × 68 8 + 9 Average = 408 + 612 17 Average = 1020 = 60 marks. 17
