A sample of 12 measurements has a mean of 34 and a standard deviation of 4.5. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 34 each.
A. Find the mean of the sample of 14 measurements.
Mean =
B. Find the standard deviation of the sample of 14 measurements.
Mean will remain unchanged as 34. but if the new values are different new mean will be computed as
12(34)+2(34)
-------------
12+2
476/14
=34
sample standard deviation
=
Part B op
20.1656
To find the mean of the sample of 14 measurements, you would need to calculate the sum of all the measurements and then divide by the total number of measurements.
The sum of the 12 measurements can be calculated by multiplying the mean (34) by the number of measurements (12):
Sum of 12 measurements = Mean * number of measurements
= 34 * 12
= 408
Since the two additional measurements have a common value of 34, their sum would be 34 + 34 = 68.
Now, to find the sum of all 14 measurements, we add the sum of the 12 measurements to the sum of the additional 2 measurements:
Sum of 14 measurements = Sum of 12 measurements + Sum of 2 additional measurements
= 408 + 68
= 476
Finally, to find the mean of the sample of 14 measurements, divide the sum of the measurements by the total number of measurements:
Mean = Sum of measurements / number of measurements
= 476 / 14
= 34
Therefore, the mean of the sample of 14 measurements is also 34.
To find the standard deviation of the sample of 14 measurements, you would need to use the formula for standard deviation. However, since the two additional measurements have the same value as the mean, the standard deviation remains unchanged. Therefore, the standard deviation of the sample of 14 measurements would still be 4.5.