Here's the five- number summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C. in the United States.
Min. = 2.5, Q1= 36, Median = 60, Q3= 100, Max. = 205
About what proportion of the states have cigarette taxes (i) greater than 36 cents and (ii) greater than $1?
joe mama
To determine the proportion of states with cigarette taxes greater than a certain amount, we need to compare the given amount with the values in the five-number summary.
(i) Proportion of states with cigarette taxes greater than 36 cents:
Looking at the five-number summary, we see that the value of Q1 (the first quartile) is 36 cents. The first quartile represents the 25th percentile, meaning that 25% of the states have cigarette taxes lower or equal to 36 cents. Therefore, the proportion of states with cigarette taxes greater than 36 cents is 1 - 0.25 = 0.75, or 75%.
(ii) Proportion of states with cigarette taxes greater than $1:
To compare the value of $1 with the five-number summary, we need to convert it to cents. Since 1 dollar is equal to 100 cents, we are looking for the proportion of states with cigarette taxes greater than 100 cents.
Looking at the five-number summary, we see that the value of Q3 (the third quartile) is 100 cents. The third quartile represents the 75th percentile, meaning that 75% of the states have cigarette taxes lower or equal to 100 cents. Therefore, the proportion of states with cigarette taxes greater than $1 (or 100 cents) is 1 - 0.75 = 0.25, or 25%.
In summary:
(i) About 75% of the states have cigarette taxes greater than 36 cents.
(ii) About 25% of the states have cigarette taxes greater than $1.