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.

The mean of 18 observations can be calculated as:

mean = (sum of observations) / (number of observations)

Let's call the original value of the mis-copied observation "x". The sum of the original 18 observations is 18 times the mean of 7, or 126. The sum of the mis-copied data is 18 times the mis-copied value of 21, or 378. The correct sum of the observations is 126 + x - 21, or 105 + x.

The correct mean of the observations is:

mean = (105 + x) / 18

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