QWhat is the corrected mean of 40 observations, given an initial mean of 46, when it is discovered that one of the observations, which was recorded as 33, should have been recorded as 38?
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Explanation
The formula for average is: average = sum of quantities / number of quantities.
In this case, the mean of 40 observations was given as 46. It was later found that one of the observations, 38, was wrongly recorded as 33.
To find the corrected mean value, we first need to calculate the sum of the 40 observations. Using the formula for average, we know that the sum of the 40 observations is 46 x 40 = 1840.
Next, we need to find the correct sum by adding the difference between the correct observation value of 38 and the wrongly recorded value of 33. The correct sum is 1840 + (38 - 33) = 1845.
Finally, we can use the formula for average to find the corrected mean value by dividing the correct sum of 1845 by the number of observations, which is 40.
This gives us a corrected mean value of 1845 / 40 = 46.125.
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