Question

Here is some data from the class data set. I have selected the first 100 responses (the "frequency" column adds up to 100). Below is the data for how many letters are in your first names and how many hours of television you reported watching (fractions were rounded up to the nearest whole number), along with how many people selected each response # Letters # Hours TV Frequency 48 12 200 | Frequency 4 23 25 18 1.S 4 10 10

The z scores for the individuals with the minimum and maximum number of letters in their first name are more similar in magnitude (in other words, their absolute values are more similar) than the z scores of the individuals with the maximum or minimum number of hours of TV watched. Why is this?

Answer 1

The frequency for 3 and 10 number of letters is 1 and 2. Similarly, frequency for 4 and 5 are also close. infact we can see that the number of letters in their first name follows symmetric distribution .

However the frequency for the number of hours of TV watched is decreasing as the number of hours increases. That is the distribution of number of hours of TV watched is asymmetric.

Hence the z scores are of same magnitude for the individuals with minimum and maximum number of letters in their first name.