Through years of careful observation, you have begun to suspect that how vocal cats are is somehow related to the average length of their whiskers. In order to determine whether or not this is true, you sample several cats that you know, measure the mean length of their whiskers, and also record how many times each cat meows during one day. Your results are presented in the table below:
Cat Mean Whisker Length (cm) Daily Meows
Buttons 10.2 27
Wally 9.8 42
Heisenberg 11.6 15
Major Major 10.4 7
Russia 9.1 18
Fygyt 10.0 25
a) After you've recorded the data for the cats, you realize that if you now include data from one more cat, Redbeard, the mean whisker length of the cats becomes 10.514 cm. What was Redbeard's mean whisker length? Please calculate your answers to 3 decimal places.
b) What is the standard deviation in whisker length for all of the cats, including Redbeard? What does this value tell you?
c) If you know that Redbeard produced 15 meows in one day, do your data (including Redbeard's data) support your idea that mean whisker length is related to vocalizations? If so, how are they related?
d) Describe the shape of the distribution of mean whisker length for your sample in terms of skewness and kurtosis. Please draw a picture (or pictures) based on your calculations, indicating what the distribution looks like.