The mean and sample standard deviation of the dataset consisting of 10 observations is 16 and 10 respectively. Later it is noted that one observation 16 is wrongly noted as 10. What is the mean of the original dataset? (Correct to 2 decimal place accuracy)
Question
The mean and sample standard deviation of the dataset consisting of 10 observations is 16 and 10 respectively. Later it is noted that one observation 16 is wrongly noted as 10. What is the mean of the original dataset? (Correct to 2 decimal place accuracy)
Solution
Step 1: Calculate the total sum of the incorrect dataset. The mean is the total sum divided by the number of observations. So, the total sum = mean * number of observations = 16 * 10 = 160.
Step 2: Find the sum of the correct dataset. The incorrect observation was 10, but it should have been 16. So, the sum of the correct dataset = total sum of incorrect dataset - incorrect observation + correct observation = 160 - 10 + 16 = 166.
Step 3: Calculate the mean of the correct dataset. The mean = total sum / number of observations = 166 / 10 = 16.6.
So, the mean of the original dataset is 16.6.
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