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The mean of 50 numbers is 30. Later it was discovered that two entries were wrongly entered as 62 and 13 instead of 26 and 31. Find the correct mean.
  • a)
    36.12
  • b)
    30.66
  • c)
    29.64
  • d)
    28.21
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The mean of 50 numbers is 30. Later it was discovered that two entries...
⇒ Sum of the number = mean × Total number = 50 × 30
⇒ Sum of the number = 1500
⇒ Difference of wrong number = 26 - 62 = -36 and 31 - 13 = 18
⇒ New sum = 1500 - 36 + 18 = 1482
⇒ Corrected mean = 1482/50
∴ Corre cted mean = 29.64
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Most Upvoted Answer
The mean of 50 numbers is 30. Later it was discovered that two entries...
Solution:
Let's first find the sum of the original 50 numbers by multiplying the mean (30) by the total number of values (50):
Sum of original 50 numbers = mean x total number of values = 30 x 50 = 1500

Next, let's find the sum of the incorrect values that were entered:
Sum of incorrect values = 62 + 13 = 75

Now, let's find the sum of the correct values:
Sum of correct values = sum of original 50 numbers - sum of incorrect values = 1500 - 75 = 1425

Since two incorrect values were entered instead of two correct values, we need to subtract the sum of the incorrect values from the sum of the correct values, and then add the correct values.
Correct sum = sum of correct values + sum of incorrect values - sum of incorrect values = 1425 + 75 - 62 - 13 = 1425

Therefore, the sum of the corrected numbers is 1425.

Finally, let's find the correct mean by dividing the sum of the corrected numbers by the total number of values:
Correct mean = sum of corrected numbers / total number of values = 1425 / 50 = 28.5

The correct mean of the 50 numbers is 28.5.

Hence, the correct answer is option C) 29.64.
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The mean of 50 numbers is 30. Later it was discovered that two entries were wrongly entered as 62 and 13 instead of 26 and 31. Find the correct mean.a)36.12b)30.66c)29.64d)28.21Correct answer is option 'C'. Can you explain this answer?
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