The mean of 20 observations is 6.21. Later on, it was discovered that the two items +5 and +3 were taken as-5 and -3. Find the correct mean.
Question
The mean of 20 observations is 6.21. Later on, it was discovered that the two items +5 and +3 were taken as-5 and -3. Find the correct mean.
Solution
Step 1: Calculate the sum of the original observations. The mean is given as 6.21 for 20 observations, so the total sum would be 6.21 * 20 = 124.2
Step 2: Correct the errors in the observations. The two items were recorded as -5 and -3, but they should have been +5 and +3. This means the total sum of the observations is off by (-5 - 3) - (5 + 3) = -16.
Step 3: Add this difference to the original sum to get the corrected sum. So, 124.2 - (-16) = 140.2
Step 4: Calculate the corrected mean by dividing the corrected sum by the number of observations. So, the corrected mean is 140.2 / 20 = 7.01.
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