Here\'s the five-number summary for the distribution of cigarette taxes (in cent
ID: 3202430 • Letter: H
Question
Here's the five-number summary for the distribution of cigarette taxes (in cents) among the 50 states in the United States.
Minimum = 2.9, Q1 = 39, Median = 60, Q3 = 102, Maximum = 210
(a) About what PROPORTION of the states have cigarette taxes greater than the following?
(i) greater than 39 cents?
(2 decimal places)
(ii) greater than $1.02?
(2 decimal places)
(b) Find the interquartile range. Interpret it.
cents (whole number)
a. The IQR provides the range for the middle half of the data.
b. The IQR provides the range for the lower half of the data.
c. The IQR provides the range for the upper half of the data.
d. The IQR provides the range within one standard deviation of the mean.
Based on the summary, do you think that this distribution was bell shaped? If so, why? If not, why not, and what shape would you expect?
Yes, the five number summary is fairly evenly spaced.
Yes, the five number summary is very spread out.
No, the distribution appears skewed to the left.
No, the distribution appears skewed to the right.
Explanation / Answer
a) i) Q1 = 39 cents
i.e. 25% data is less than 39 cents and 75 % data is greater than 39 cents.
P(cigarette taxes greater than 39 cents) = 0.75
a) ii) Q3 = 102 cents = $ 1.02
i.e. 75% data is less than $ 1.02 and 25 % data is greater than $ 1.02.
P(cigarette taxes greater than $ 1.02 ) = 0.25
................................................................................................................................
b) interquartile range (IQR) = Q3 - Q1 = 102-39 = 63 cents
Interpretation
a. The IQR provides the range for the middle half of the data.
......................................................................................................................................
Based on the summary, do you think that this distribution was bell shaped?
No, the distribution appears skewed to the right.
Since the median is closer to Q1 and Q3 is far away.
..........................................................................................................................................................