Question

Data on snakes. For a biology project, you measure the length (inches) and weight (ounces) of 28 snakes of the same variety. What units of measurement do each of the following have? (units of measurement can be inches for length or height, pounds for weight, acres for areas, etc. This is not a multiple-choice question. For each of the following write the units. You don’t need to know the numbers for this.) A) The mean length of the snakes. B) The first quartile of the snake lengths. C) The standard deviation of the snake lengths. D) The correlation between length and snake weight. E) Suppose that the correlation between length and weight turns out to be r = 0.6. If you were to measure length in centimeters instead of inches, what would be the new value of r? (one inch is 2.54 centimeters) F) A fellow student of yours at the biology department went on an expedition in NJ and collected length measurements for 28 snakes. Based on her calculations the average length of the snakes she caught is 2.3 feet and the standard deviation 2.5 feet. Do you have any reason to believe that her calculations are wrong? Explain your reasoning.

Answer 1

A) The mean length of the snakes.

We have the units for lengths as inches. The mean is sum of all observations dividing by the no. of observations. So we are just summing the lengths, the mean will therefore also have 'inches'.

B) The first quartile of the snake lengths.

The first quartile is a values below which 25% of the data lies. It is a value from the data. So it is going to be a length. It's units will be 'inches'.

C) The standard deviation of the snake lengths.

SD is the average of deviations from the mean. So again we are first summing the deviations which have units in inches and then dividing by the observations. We actually square the deviations and then take the mean and take its square root. So the units remain the same. inches.

D) The correlation between length and snake weight.

Correlation =

Numerator is the covariance, so its units will be 'weight * inches'. In the denominator, we multiply units of weight and length so in the denominator again the units will be 'weight * inches'. These units will be divide and their answer will be '1' That is no units.  

E) Suppose that the correlation between length and weight turns out to be r = 0.6. If you were to measure length in centimeters instead of inches, what would be the new value of r? (one inch is 2.54 centimeters)

Since there is no units for correlation, it doesn't matter how the data is collected. Since if length is measured in cms, the units for numerator and denominator will be ' 'weight * cm'. They will again cancel out with no units for correlation.

F) A fellow student of yours at the biology department went on an expedition in NJ and collected length measurements for 28 snakes. Based on her calculations the average length of the snakes she caught is 2.3 feet and the standard deviation 2.5 feet. Do you have any reason to believe that her calculations are wrong? Explain your reasoning.

There is nothing wrong with calculations. If the data is recorded in feet then both SD and mean will be in fee. She can convert the data from feet to inches where 1 feet = 12 inches. The SD is very high that it is higher than the mean. This simply means that the snakes length vary a lot.