A sample of 12 measurements has a mean of 39 and a standard

A sample of 12 measurements has a mean of 39 and a standard deviation of 3. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 39 each.

A. Find the mean of the sample of 14 measurements

B. Find the standard deviation of the sample of 14 measurements.(please explain how to obtain the deviation step by step)

Solution

A) AS WE HAVE ADDED THE TWO WITH MEASUREMENTS = 39 EACH

AND THE MEAN IS 39

IF WE ADD ANU NUMBER OF ITEMS WITH MEASUREMENT EQUAL TO THE MEAN THEN THE MEAN WILL REMAIN SAME.

HENCE IN THIS CASE THE MEAN WIL BE 39

B)

B. Old Var = 3^2 = 9, then Old SSQ = 9*12 = 108
Hence new Var = 108/14 = 7.71
Hence new SD = 2.77