There are four cars at Hogwarts, and this year this is the number of drivers for
ID: 3306997 • Letter: T
Question
There are four cars at Hogwarts, and this year this is the number of drivers for each: Nissan- 76; Honda - 82; Chevy - 61; Porsche - 73
a) What is the median number of driversfor the car? (Note this is a parameter as all four cars are included.)
b) List all of the possible samples of size two. This is with replacement, so there should be 16 of them. For each of these, find the sample median.
c) Take all the sample medians you found in step b. Find the mean of these sample medians.
d) Is that mean of sample medians (from part c) the same as the population median (from part a) e) Why or why not? Explain why you got the result you did in part d.
Please explain every step fully for full rating! Thank you
Explanation / Answer
(a)
The median number of drivers is: (73+76)/2 = 74.5
(b)
The possible samples along with their medians are:
(i) Nissan, Nissan : 76
(ii) Nissan, Honda : 79
(iii) Nissan, Chevy : 68.5
(iv) Nissan, Porsche : 74.5
(v) Honda, Honda : 82
(vi) Honda, Nissan : 79
(vii) Honda, Chevy: 71.5
(viii) Honda, Porsche : 77.5
(ix) Chevy, Chevy: 61
(x) Chevy, Honda: 71.5
(xi) Chevy, Nissan: 68.5
(xii) Chevy, Porsche : 67
(xiii) Porsche, Nissan : 74.5
(xiv) Porsche, Chevy : 67
(xv) Porsche, Honda : 77.5
(xvi) Porsche, Porsche : 73
Hope this helps !
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