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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