Question

Here is the five-number summary for the distribution of a cigarette tax (in cents) for all the states in a certain country Use this information to answer pans a through d Minimum = 6. Q1 =40 Median = 72. Q3= 103. Maximum = 137

a). About what proportion of the states have cigarette taxes (i) greater than 40 cents and (ii) greater than 103 cents?
(i) About of the states have cigarette taxes greater than 40 cents.
(ii) About of the states have cigarette taxes greater than 103 cents.
b). Between what two values are the middle 50% of the observations found?
The lower bound of the middle 50% is [] and the upper bound of the middle 50% is {Type a whole number)
c). Find and interpret the interquartile range The interquartile range () is What is the relevance of the IQR?
A. The IQR summarizes the range for the lower half of the data.
B. The IQR summarizes the range for the middle half of the data
C. The IQR summarizes the range within one standard deviation of the mean
D. The IQR summarizes the range for the upper half of the data
d). Based on the summary, do you think this distribution was bell-shaped? If so. why? If not. why not. and what shape would you expect?
A. The distribution is skewed left because the median is closer to Q3. Further proof is given by the values of the minimum and maximum relative to Q1 and Q3. respectively.
B. The distribution is bell-shaped because the median is exactly between Q1 and Q3 Further proof is given by the values of the minimum and maximum relative to Q1 and Q3 respectively
C. The distribution is skewed right because the median is closer to Q1 Further proof is given by the values of the minimum and maximum relative to Q1 and Q3 respectively.

Answer 1

The five-number summary suggests that 75% of the states have cigarette taxes greater than 40 cents, 25% greater than 103 cents. The middle 50% (IQR) lies between 40 and 103 cents, amounting to an IQR of 63 cents, summarizing the range for the middle half of data. The distribution is likely skewed right.

Step-by-step explanation:

Regarding the five-number summary for the distribution of a cigarette tax, let's answer the questions part by part:

a) Proportion of states with cigarette taxes greater than certain amounts:

b) Middle 50% of observations:

The middle 50%

of the observations, also known as the

interquartile range (IQR)

, is found between Q1 and Q3. Therefore, the lower bound is

40 cents

and the upper bound is

103 cents

c) Interquartile range (IQR) and its interpretation:

The IQR is 103 - 40 = 63 cents. The relevance of the IQR is B, which means IQR summarizes the range for the middle half of the data.

d) Distribution shape analysis:

Given the information, and assuming symmetry around the median, one might expect the distribution to be skewed right because the median is closer to Q1 and the maximum is much farther from Q3 than the minimum is from Q1, which is indicative of a longer tail on the right side (C).