QuestionGiven the five-number summary of cigarette taxes (in cents): Min=6, Q1=37, Median=88, Q3=105, Max=118. Answer parts a & b. a. Proportion of states with taxes: (i) >37 cents is about , (ii) >105 cents is about . b. Middle of observations lies between Q1 and Q3: lower bound is 37, upper bound is 105.
Studdy Solution
STEP 1
Assumptions1. The minimum cigarette tax is6 cents.
. The first quartile (Q1) is37 cents.
3. The median is88 cents.
4. The third quartile (Q3) is105 cents.
5. The maximum cigarette tax is118 cents.
STEP 2
For part a, we use the definition of quartiles to determine the proportion of states with cigarette taxes greater than certain values.(i) Q1 represents the value below which25% of the data falls. Therefore, the proportion of states with cigarette taxes greater than37 cents (Q1) is75%.
(ii) Q represents the value below which75% of the data falls. Therefore, the proportion of states with cigarette taxes greater than105 cents (Q) is25%.
STEP 3
For part b, the middle50% of the observations are found between Q1 and Q3.The lower bound of the middle50% is Q1 and the upper bound of the middle50% is Q3.
So, the middle50% of the observations are found between37 cents and105 cents.
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