Average
- The average of 10 items was found to be 80 but while calculating, one of the items was counted as 60 instead of 50. Then the correct average would havebeen :
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Given that , The average of 10 items = 80
While calculating, one of the items was counted as 60 instead of 50 , thenCorrected mean = 80 × 10 - 60 + 50 10 Corrected mean = 800 - 10 = 790 10 10
Corrected mean = 79
Second method to solve this question with the help of given formula :
Here, n = 10, m = 80 , a = 50, b = 60
Correct Option: C
Given that , The average of 10 items = 80
While calculating, one of the items was counted as 60 instead of 50 , thenCorrected mean = 80 × 10 - 60 + 50 10 Corrected mean = 800 - 10 = 790 10 10
Corrected mean = 79
Second method to solve this question with the help of given formula :
Here, n = 10, m = 80 , a = 50, b = 60Correct Average = m + (a - b) n Correct Average = 80 + (50 - 60) 10
Correct Average = 80 – 1 = 79
- The mean value of 20 observations was found to be 75, but later on it was detected that 97 was misread as 79. Find the correct mean.
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Later on it was detected that 97 was misread as 79 .
Then ,Difference = 97 – 79 = 18True average = 75 + 18 20
True average = 75.9
Second method to solve this question with the help of given formula :
Here, n = 20, m = 75 , a = 97, b = 79Correct Average = m + (a - b) n
Correct Option: C
Later on it was detected that 97 was misread as 79 .
Then ,Difference = 97 – 79 = 18True average = 75 + 18 20
True average = 75.9
Second method to solve this question with the help of given formula :
Here, n = 20, m = 75 , a = 97, b = 79Correct Average = m + (a - b) n Correct Average = 75 + (97 - 79) 20 Correct Average = 75 + 18 20
Correct Average = 75 + 0.9 = 75.9
- The mean of 20 items is 47. Later it is found that the item 62 is wrongly written as 26. Find the correct mean.
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Later it is found that the item 62 is wrongly written as 26 ,
∴ Difference = 62 – 26 = 36∴ Required average = 47 + 36 20
Required average = 47 + 1.8 = 48.8
Second method to solve this question with the help of given formula :
Here, n = 20 , m = 47 , a = 62 , b = 26Correct Average = m + (a - b) n
Correct Option: A
Later it is found that the item 62 is wrongly written as 26 ,
∴ Difference = 62 – 26 = 36∴ Required average = 47 + 36 20
Required average = 47 + 1.8 = 48.8
Second method to solve this question with the help of given formula :
Here, n = 20 , m = 47 , a = 62 , b = 26Correct Average = m + (a - b) n Correct Average = 47 + (62 - 26) 20 Correct Average = 47 + 36 20
Correct Average = 47 + 1.8 = 48.8
- A tabulator while calculating the average marks of 100 students of an examination, by mistake enters 68, instead of 86 and obtained the average as 58; the actual average marks of those students is
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On the basis of given details in question , we have
Difference = 86 – 68 = 18∴ Actual average = 58 + 18 100
Actual average = 58.18
Second method to solve this question with the help of given formula :
Here, n = 100 , m = 58 , a = 86 , b = 68Correct Average = m + (a - b) n
Correct Option: A
On the basis of given details in question , we have
Difference = 86 – 68 = 18∴ Actual average = 58 + 18 100
Actual average = 58.18
Second method to solve this question with the help of given formula :
Here, n = 100 , m = 58 , a = 86 , b = 68Correct Average = m + (a - b) n Correct Average = 58 + (86 - 68) 100
Correct Average = 58 + 18 100
Correct Average = 58 + 0.18 = 58.18
- Mean of 10 numbers is 30. Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32. The correct mean is
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Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32 .
∴ Difference = 15 + 23 – 51 – 32 = –45∴ Correct average = 30 - 45 = 25.5 10
Second method to solve this question with the help of given formula :
Here, n = 10, m = 30 , a = 15, b = 23 , p = 51 , q = 32Correct Average = m + (a + b - p - q) n Correct Average = 30 + (15 + 23 - 51 - 32) 10
Correct Option: A
Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32 .
∴ Difference = 15 + 23 – 51 – 32 = –45∴ Correct average = 30 - 45 = 25.5 10
Second method to solve this question with the help of given formula :
Here, n = 10, m = 30 , a = 15, b = 23 , p = 51 , q = 32Correct Average = m + (a + b - p - q) n Correct Average = 30 + (15 + 23 - 51 - 32) 10 Correct Average = 30 + 
38 - 83 
10 Correct Average = 30 - 45 = 25.5 10
Correct Average = 30 – 4.5 = 25.5
