In a biology lab, a student has measured the lengths of 30 palmetto bugs in inches. He computes the mean and standard deviation as 4.1 inches and 1.2 inches, respectively. He later finds out that he was supposed to calculate the mean and standard deviation in centimeters instead of in inches. What are the new mean and standard deviation of his sample, in centimeters? (Note: 1 in = 2.54 cm)
1 Answer
You can just convert from inches to centimeters.
Let's say he first converts all his individual measurements. They would then all be 'inflated' by a factor of 2.54. If he then calculated the mean and standard deviation again, these would also come out a factor of 2.54 higher.
So he might as well convert just the mean and SD.
These will then be 10.4 cm and 3.0 cm.
Note
There is a small possible problem though:
Since the cm is a smaller unit than the inch, we may introduce some false accuracy here.
*Explanation by example:***
4.1 inches means the true value is between 4.05 and 4.15 inches
In centimeters this means between 10.29 and 10.54.
And the 10.4 cm above suggests between 10.35 and 10.45
If means and SD are available before rounding down to 1 decimal, it is better to convert from them, and rounding down the cm.
