What is the standard deviation of the new data shifted by 5 mmHg?

Question

1.     Suppose you measure the blood pressure of 100 hypertensive males and find that they have a mean systolic blood pressure of 133 mm Hg with a variance of 16 mm Hg. You later discover that your blood pressure monitor was calibrated incorrectly. To adjust for this mistake, you subtract 5 mm Hg from each male’s systolic blood pressure. What is the standard deviation of the new data shifted by 5 mmHg?

Answer 1

The variance is exactly the same value of 16 and the standard deviation is exactly the same value of 4. Although it's straightforward to show this using expected value operations, it is also easy to just demonstrate using words. Here's several options:

1) Every observation moved by the same amount in the same direction. This means that the mean moved by the same amount in the same direction. If the observations and their means moved the same distance in the same direction, the distance between observation and the mean remains the same. Since it's that distance that is used to calculate the standard deviation, everything that goes into the required formula is exactly the same, resulting in the same standard deviation.

2) The standard deviation measures the spread of the data. If all the data is shifted by the same amount in the same direction, the spread of the data hasn't been altered. Only the location of the data has been altered. If the actual spread hasn't changed, the standard deviation will be the same.