Mean and Standard deviation of 18 observations are found to be 7 and 4, respectively. On comparing the original data, it was found that an observation 12 was miscopied as 21 in the calculations. Calculate correct mean and standard deviation.

To correct the mean and standard deviation after identifying an error in the data, we need to first correct the mistaken observation, then recalculate the mean and standard deviation.

Let's denote:
- n = 18 (number of observations)
- Σx = sum of all observations
- μ = original mean
- σ = original standard deviation
- x_mistake = the mistaken observation (21)
- x_corrected = the corrected observation (12)

Given:
- Original mean (μ) = 7
- Original standard deviation (σ) = 4

We can use the formula for the sum of observations:
Σx = n * μ

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