Question

Suppose that the sample mean of 12 data points is 25. It is discovered that a data point having value 16 was incorrectly read as 19. What is the revised value of the sample mean?

Answer 1

The correct mean is `bar(x_c)=24.75`. See explanation.

Explanation:

From the text we know that:

• the number of data is `n=12`

• the incorrect mean is `bar(x)=25`

• one of the values is `19` but should be `16`.

From the first two points we can calculate that the sum of values is:

`S=n*bar(x)=12*25=300`

Now we have to "correct" the misread value. This means we have to subtract the incorrectly read value and add the corrected one:

`S_c=S-19+16=300-19+16=300-3=297`

The number of values did not change so to calculate the correct mean we have to divide this number by `n`:

`bar(x_c)=S_c/n=297/12=24.75`.

Answer: The corrected mean is `24.75`