Question

And now, for the Dog-and-Pony Show!

Consider the following scenario and calculate descriptive statistics to answer the accompanying questions:

Clydesdale horses have a mean height of 16.5 hands with a standard deviation of 1.85 hands;

Great Danes (a breed of dog) have a mean height of 81 cm with a standard deviation of 13 cmm.

1. Which population exhibits greater relative variation in height?

2.Which of these two animals is taller compared to its respective breed: a 20.2 hand tall Clydesdale horse or a 107 cm tall Great Dane?

Answer 1

(1) The relative variation will be calculated using the coefficient of variation (CV) formula, which is equal to standard deviation divided by the mean and then multiplying it by 100.
Now, for Clydesdale horses, the CV value = (1.85/16.5) * 100 = 11.21.
For Great Danes, the CV value = (13/81) * 100 = 16.05.
Since the Great Danes have a higher CV value, their population exhibits greater relative variation in height.

(2) This can be done by calculating the z-score, which is calculated by subtracting the mean from the raw score and dividing it by standard deviation.
For Clydesdale horses, the z-score = (20.2 - 16.5)/1.85 = 2.00.
For Great Danes, the z-score = (107 - 81)/13 = 2.00.
Since the z-scores are exactly the same, no animal is taller than the other. They are relatively of the same size.