Finding the Correct Mean
We are given the mean of 20 observations and one incorrectly recorded value. We need to calculate the correct mean.
Initial Calculation
- Calculate the original sum of the 20 observations.
Original Sum = Original Mean $\times$ Number of Observations
Original Sum = $22.5 \times 20 = 450$
- Determine the difference between the correct value and the wrong value.
Wrong value = $-25$
Correct value = $25$
Difference = Correct value $-$ Wrong value
Difference = $25 - (-25) = 25 + 25 = 50$
- Calculate the correct sum of the observations.
Correct Sum = Original Sum + Difference
Correct Sum = $450 + 50 = 500$
- Calculate the correct mean using the correct sum and the number of observations.
Correct Mean = $\frac{\text{Correct Sum}}{\text{Number of Observations}}$
Correct Mean = $\frac{500}{20} = 25$
Conclusion
The correct mean of the 20 observations is 25.
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Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
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Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
