1. To start, the 19 people who said Yes to reporting cheating reported the follo

Question

1. To start, the 19 people who said Yes to reporting cheating reported the following number of alcoholic drinks per week:

1 0 1 0 0 5 0 0 0 4 0 20 0 0 0 0 0 0 1

Calculate the following summary measures for these 19 people (show all work).

(a) Average number of drinks per week

(b) Median number of drinks per week (50th percentile)

(c) 25th percentile of drinks per week

(d) 75th percentile of drinks per week

(e) Do you think mean or the median is the best summary of the “middle/center”? Why?

(f) If you removed the person who drinks 20 alcoholic drinks per week, how do your values from (a), (b), (c), (d), change? (don’t need to recalculate; just describe)

Explanation / Answer

putting above data in ascending order:

a)

average =32/19 =1.68

b)

median =(n+1)/2 th value =(19+1)/2 th value =10th value =0

c)

25th percentiel =(n+1)/4 th value =5 th value =0

d)

75 th percentile =3(n+1)/4 th value =15 th value =1

e)

as the data seems to be right skewed as median is less than mean and not symmetric; theefore median is best summary me

f)

if we remove 20 alcoholic drinks per week ; mean will change drastically as it is not resistant to outliers; while median; 25th percentile and 75 th percentile will remain same as they does not depend on weight of values but on position,

s. no x 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 1 15 1 16 1 17 4 18 5 19 20 total 32 average= 1.684211

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